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BEGIN:VEVENT
SUMMARY:Georgios Dosidis (University of Missouri\, Columbia)
DTSTART:20201008T134000Z
DTEND:20201008T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/1/">Linear and multilinear spherical maximal functions</a>\nby G
 eorgios Dosidis (University of Missouri\, Columbia) as part of Function sp
 aces\n\n\nAbstract\nThe classical spherical maximal function is an analogu
 e of the Hardy-Littlewood maximal function that involves averages over sph
 eres instead of balls. We will review the classical bounds for the spheric
 al maximal function obtained by Stein and explore their implications for p
 artial differential equations and geometric measure theory. The main focus
  of this talk is to discuss recent results on the multilinear spherical ma
 ximal function and on a family of operators between the Hardy-Littlewood a
 nd the spherical maximal function. We will cover boundedness and convergen
 ce results for these operators for the optimal range of exponents. We will
  also include a discussion on Nikodym-type sets for spheres and spherical 
 maximal translations.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Breit (Heriot-Watt University\, Edinburgh)
DTSTART:20201022T134000Z
DTEND:20201022T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/2/">Optimal Sobolev embeddings for symmetric gradients (joint wo
 rk with Andrea Cianchi)</a>\nby Dominic Breit (Heriot-Watt University\, Ed
 inburgh) as part of Function spaces\n\n\nAbstract\nI will present an unifi
 ed approach to embedding theorems for Sobolev type spaces of vector-valued
  functions\, defined via their symmetric gradient. The Sobolev spaces in q
 uestion are built upon general rearrangement-invariant norms. Optimal targ
 et spaces in the relevant embeddings are determined within the class of al
 l rearrangement-invariant spaces. In particular\, I show that all symmetri
 c gradient Sobolev embeddings into rearrangement-invariant target spaces a
 re equivalent to the corresponding embeddings for the full gradient built 
 upon the same spaces.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Cruz-Uribe\, OFS (University of Alabama\, Tuscaloosa)
DTSTART:20201015T134000Z
DTEND:20201015T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/3/">Norm inequalities for linear and multilinear singular integr
 als on weighted and variable exponent Hardy spaces</a>\nby David Cruz-Urib
 e\, OFS (University of Alabama\, Tuscaloosa) as part of Function spaces\n\
 n\nAbstract\nI will discuss recent work with Kabe Moen and Hanh Nguyen on 
 norm inequalities of the form\n$$T\\colon H^{p_1}(w_1)\\times H^{p_2}(w_2)
 \\to L^p(w)\,$$\nwhere $T$ is a bilinear Calderón-Zygmund singular integr
 al operator\, $0 < p\, p_1\, p_2 <\\infty$ and\n$$\\frac1{p_1} + \\frac1{p
 _2} = \\frac1p\,$$\nthe weights $w\, w_1\, w_2$ are Muckenhoupt weights\, 
 and the spaces $H^{p_i}(w_i)$ are the weighted Hardy spaces introduced by 
 Stromberg and Torchinsky.\nWe also consider norm inequalities of the form\
 n$$T\\colon H^{p_1(\\cdot)} \\times H^{p_2(\\cdot)} \\to L^{p(\\cdot)}\,$$
 \nwhere $L^{p(\\cdot)}$ is a variable Lebesgue space (intuitively\, a clas
 sical Lebesgue space with the constant exponent p replaced by an exponent 
 function $p(\\cdot)$) and the spaces $H^{p_i(\\cdot)}$ are the correspondi
 ng variable exponent Hardy spaces\, introduced by me and Li-An Wang and in
 dependently by Nakai and Sawano.\nTo illustrate our approach we will consi
 der the special case of linear singular integrals. Our proofs\, which are 
 simpler than existing proofs\, rely heavily on three things: finite atomic
  decompositions\, vector-valued inequalities\, and the theory of Rubio de 
 Francia extrapolation.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Lesnik (Poznan University of Technology)
DTSTART:20201029T144000Z
DTEND:20201029T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/4/">Factorization of function spaces and pointwise multipliers</
 a>\nby Karol Lesnik (Poznan University of Technology) as part of Function 
 spaces\n\n\nAbstract\nGiven two function spaces $X$ and $Y$ (over the same
  measure space)\, we say that $X$ factorizes $Y$ if  each $f\\in Y$ may be
  written as a product \n\\[\nf=gh \\ \\ {\\rm \\ for\\ some\\ } g\\in X {\
 \rm \\ and\\ } h\\in M(X\,Y)\,\n\\]\nwhere $M(X\,Y)$ is the space of point
 wise multipliers from $X$ to $Y$. \n\nDuring the lecture I will present re
 cent developments in the subject of factorization. The problem whether one
  space may be factorized by another will be discussed for general function
  lattices as well as  for special classes of function spaces. \nMoreover\,
  it will be explained why the developed methods may be regarded as a kind 
 of arithmetic of function spaces.  Finally\, the problem of regularization
 s for factorization will be presented together with a number of applicatio
 ns.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irshaad Ahmed (Sukkur IBA University)
DTSTART:20201105T144000Z
DTEND:20201105T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/5/">On Limiting Approximation Spaces with Slowly Varying Functio
 ns</a>\nby Irshaad Ahmed (Sukkur IBA University) as part of Function space
 s\n\n\nAbstract\nThis talk is concerned with limiting approximation spaces
  involving slowly varying functions\, for which we establish some interpol
 ation formulae via limiting reiteration. An application to Besov spaces is
  given.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gord Sinnamon (University of Western Ontario\, London)
DTSTART:20201112T144000Z
DTEND:20201112T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/6/">A Normal Form for Hardy Inequalities</a>\nby Gord Sinnamon (
 University of Western Ontario\, London) as part of Function spaces\n\n\nAb
 stract\nLet $b$ be a non-negative\, non-increasing function on $(0\,\\inft
 y)$ and let $H_bf(x) =\\int_0^{b(x)}f$. The inequality $\\|H_bf\\|q\\le C\
 \|f\\|_p$ expresses the boundedness of this operator from unweighted $L^p(
 0\,\\infty)$ to unweighted $L^q(0\,\\infty)$. It is called a <i>normal for
 m Hardy inequality</i>.\n \nAn abstract formulation of a Hardy inequalitie
 s is given and every abstract Hardy inequality is shown to be equivalent\,
  in a strong sense\, to one in normal form. This equivalence applies to Ha
 rdy operators and their duals of the weighted continuous\, weighted discre
 te\, and general measures types\, as well as those based on averages over 
 starshaped sets in many dimensions. A straightforward formula relates each
  Hardy inequality to its normal form parameter $b$.\n \nBesides giving a u
 niform treatment of many different types of Hardy operator\, the reduction
  to normal form provides new insights\, simple proofs of known theorems\, 
 and new results concerning best constants.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Cianchi (University of Florence)
DTSTART:20210107T140000Z
DTEND:20210107T150000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/7/">Optimal embeddings for fractional-order Orlicz-Sobolev space
 s</a>\nby Andrea Cianchi (University of Florence) as part of Function spac
 es\n\n\nAbstract\nThe optimal Orlicz target space is exhibited for embeddi
 ngs of fractional-order Orlicz-Sobolev spaces in the Euclidean space. An i
 mproved embedding with an Orlicz-Lorentz target space\, which is optimal i
 n the broader class of all rearrangement-invariant spaces\, is also establ
 ished. Both spaces of order less than one\, and higher-order spaces are co
 nsidered. Related Hardy type inequalities are proposed as well. This is a 
 joint work with A. Alberico\, L. Pick and L. Slavíková.\n\nPlease be awa
 re that this seminar starts at an unusual time (40 mins earlier).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Diening (Bielefeld University)
DTSTART:20201119T144000Z
DTEND:20201119T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/8/">Elliptic Equations with Degenerate Weights</a>\nby Lars Dien
 ing (Bielefeld University) as part of Function spaces\n\n\nAbstract\nWe st
 udy the regularity of the weighted Laplacian and $p$-Laplacian with\ndegen
 erate elliptic matrix-valued weights.  We establish a novel\nlogarithmic B
 MO-condition on the weight that allows to transfer higher\nintegrability o
 f the data to the gradient of the solution. The\nsharpness of our estimate
 s is proved by examples.\n\nThe talk is based on joint work with Anna Balc
 i\, Raffaella Giova and\nAntonia Passarelli di Napoli.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Lang (The Ohio State University)
DTSTART:20201126T144000Z
DTEND:20201126T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/9/">Extremal functions for Sobolev Embedding and non-linear prob
 lems</a>\nby Jan Lang (The Ohio State University) as part of Function spac
 es\n\n\nAbstract\nWe will focus on extremal functions for Sobolev Embbedin
 gs of first and second order and at the eigenfunctions and eigenvalues of 
 corresponding non-linear problems (i.e. $pq$-Laplacian and $pq$-bi-Laplaci
 an on interval or rectangular domain). The main results will be the full c
 haracterization of spectrum for corresponding non-linear problems\, geomet
 rical properties of eigenfunctions and their connection with Approximation
  theory.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Kalamajska (University of Warsaw)
DTSTART:20201203T144000Z
DTEND:20201203T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/10/">Strongly nonlinear multiplicative inequalities</a>\nby Agni
 eszka Kalamajska (University of Warsaw) as part of Function spaces\n\n\nAb
 stract\nIn 2012  together with Jan Peszek we obtained the following inequa
 lity:\n$$\n  \\int_{(a\,b)} |f^{'}(x)|^qh(f(x))dx \\le\n   C \\int_{(a\,b)
 }\n    \\left( \\sqrt{|f^{''}(x){\\mathcal T}_{h}(f(x))| }\\right)^qh(f(x)
 )dx\,\n\\tag{1}\n$$\n  as well as  its Orlicz  variants\,\n  where ${\\mat
 hcal T}_{h}(\\cdot)$ is certain transformation of function  $f$ with the p
 roperty ${\\mathcal T}_{\\lambda^\\alpha}(f)\\sim f$\, generalizing previo
 us results in this direction due to Mazja.\n\nInequalities in the form (1)
  were further generalized  in several directions in the chain of my joint 
 works  with Katarzyna Pietruska-Paluba\, Jan Peszek\, Katarzyna Mazowiecka
 \, Tomasz Choczewski\, Ignacy Lipka and with Alberto Fiorenza and  Claudia
  Capogne\, Tomáš Roskovec and Dalmil Peša.\n\n I will discuss various v
 ersions of inequality (1)\, together with its multidimensional variants.\n
  We will also show some applications of such inequalities to the regularit
 y theory for degenerated PDE’s of elliptic type.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Molchanova (University of Vienna)
DTSTART:20201217T144000Z
DTEND:20201217T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/11/">An extended variational approach for nonlinear PDE via modu
 lar spaces</a>\nby Anastasia Molchanova (University of Vienna) as part of 
 Function spaces\n\n\nAbstract\nLet $H$ be a Hilbert space and $\\varphi\\c
 olon H \\to [0\,\\infty]$ be a convex\, lower-semicontinuous\, and proper 
 modular.\nWe study an evolution equation\n$$\n  \\partial_t u + \\partial 
 \\varphi (u) \\ni f\, \\qquad u(0)=u_0\n\\tag{1}\n$$\nfor $t\\in[0\,T]$ an
 d $f\\in L^1(0\,T\;H)$.\nIf $u_0\\in H$ and $\\partial \\varphi$ is consid
 ered as a nonlinear operator from $V$ to $V^*$\, for some separable and re
 flexive $V\\subset H$\,\none can apply the classical variational approach 
 to obtain well-posedness of problem (1).\nIn this talk\, we present a more
  general method\, which allows to treat (1) in nonseparable or nonreflexiv
 e cases of modular spaces $L_{\\varphi}$ instead of $V$.\n\nThis is a join
 t work with A. Menovschikov and L. Scarpa.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Alberico (Italian National Research Council\, Naples)
DTSTART:20210114T144000Z
DTEND:20210114T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/12/">Limits of fractional Orlicz-Sobolev spaces</a>\nby Angela A
 lberico (Italian National Research Council\, Naples) as part of Function s
 paces\n\n\nAbstract\nWe establish versions for fractional Orlicz-Sobolev s
 eminorms\, built upon Young functions\, of the Bourgain-Brezis-Mironescu t
 heorem on the limit as $s\\to 1^-$\, and of the Maz’ya-Shaposhnikova the
 orem on the limit as $s\\to 0^+$\, dealing with classical fractional Sobol
 ev spaces. As regards the limit as $s\\to 1^-$\, Young functions with an a
 symptotic linear growth are also considered in connection with the space o
 f functions of bounded variation. Concerning the limit as $s\\to 0^+$\, Yo
 ung functions fulfilling the $\\Delta_2$-condition are admissible. Indeed\
 , counterexamples show that our result may fail if this condition is dropp
 ed. This is a joint work with Andrea Cianchi\, Luboš Pick and Lenka Slav
 íková.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Evseev (Steklov Mathematical Institute\, Moscow)
DTSTART:20210121T144000Z
DTEND:20210121T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/13/">Vector-valued Sobolev spaces based on Banach function space
 s</a>\nby Nikita Evseev (Steklov Mathematical Institute\, Moscow) as part 
 of Function spaces\n\n\nAbstract\nIt is known that for Banach valued funct
 ions there are several approaches to define a Sobolev class. We compare th
 e usual definition via weak derivatives with the Reshetnyak-Sobolev space 
 and with the Newtonian space\; in particular\, we provide sucient conditi
 ons when all three agree. As well we revise the difference quotient criter
 ion and the property of Lipschitz mapping to preserve Sobolev space when i
 t acting as a superposition operator.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Winfried Sickel (Friedrich Schiller University\, Jena)
DTSTART:20210128T144000Z
DTEND:20210128T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/14/">Complex Interpolation of Smoothness Spaces built on Morrey 
 Spaces</a>\nby Winfried Sickel (Friedrich Schiller University\, Jena) as p
 art of Function spaces\n\n\nAbstract\nLet  $\\mathcal{M}_p^u([0\,1]^d)$ de
 note the Morrey space on the cube $[0\,1]^d$ and $[\\\, \\cdot\\\, \, \\\,
  \\cdot\\\,]_\\Theta$\, $0 < \\Theta <1 $\, \nrefers to the complex method
  of interpolation. We shall discuss generalizations of the formula \n\\[\n
 \\left[\\mathcal{M}^{u_0}_{p_0}([0\,1]^d)\,\\\,\\mathcal{M}^{u_1}_{p_1}([0
 \,1]^d)\\right]_\\Theta = \\overset{\\diamond}{\\mathcal{M}_p^u}([0\,1]^d)
 \\\, \,\n\\]\nif\n\\[\n1\\le p_0 < u_0 <\\infty\, \\quad 1 < p_1< u_1 <\\i
 nfty\, \\quad p_0 < p_1\,\n\\quad 0 < \\Theta < 1\n\\]\nand\n\\[\np_0\\\, 
 \\cdot\\\,  u_1 = p_1\\\, \\cdot \\\,  u_0\\\, \, \\quad\n\\frac1p:=\\frac
 {1-\\Theta}{p_0}+\\frac{\\Theta}{p_1}\\\, \, \\quad\n\\frac1u:=\\frac{1-\\
 Theta}{u_0}+\\frac{\\Theta}{u_1}\\\, .\n\\]\nFor a domain $ \\Omega \\subs
 et \\mathbb{R}^d$ the space $\\overset{\\diamond}{\\mathcal{M}_p^u}(\\Omeg
 a)$ is defined as the closure of the smooth \nfunctions with respect to th
 e norm of the space $\\mathcal{M}_p^u(\\Omega)$.\nThe generalizations will
  include more general bounded domains (Lipschitz domains) and more general
  function spaces\n(Lizorkin-Triebel-Morrey spaces). \n\n \nMy talk will be
  based on joint work with Marc Hovemann (Jena) and \nCiqiang Zhuo (Changsh
 a).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Behnam Esmayli (University of Pittsburgh)
DTSTART:20201210T144000Z
DTEND:20201210T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/15/">Co-area formula for maps into metric spaces</a>\nby Behnam 
 Esmayli (University of Pittsburgh) as part of Function spaces\n\n\nAbstrac
 t\nCo-area formula for maps between Euclidean spaces contains\, as its ver
 y special cases\, both Fubini's theorem and integration in polar coordinat
 es formula.\n          In 2009\, L. Reichel proved the coarea formula for 
 maps from Euclidean spaces to general metric spaces. I will discuss a new 
 proof of the latter by the way of an implicit function theorem for such ma
 ps.\n          An important tool is an improved version of the coarea ineq
 uality (a.k.a Eilenberg inequality) that was the subject of a recent joint
  work with Piotr Hajlasz.\n          Our proof of the coarea formula does 
 not use the Euclidean version of it and can thus be viewed as new (and arg
 uably more geometric) in that case as well.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Pérez (Basque Center for Applied Mathematics)
DTSTART:20210204T144000Z
DTEND:20210204T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/16
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/16/">Fractional Poincaré inequalities and Harmonic Analysis</a>
 \nby Carlos Pérez (Basque Center for Applied Mathematics) as part of Func
 tion spaces\n\n\nAbstract\nIn this mostly  expository lecture\,  we will d
 iscuss some recent results concerning fractional Poincaré and Poincaré-S
 obolev inequalities with weights\, the degeneracy. These results improve s
 ome well known estimates due to Fabes-Kenig-Serapioni  from the 80's in co
 nnection with the local regularity of solutions of  degenerate elliptic eq
 uations and also some more recent results by\nBourgain-Brezis-Minorescu.  
 Our approach is different from the usual ones and it is based on methods t
 hat come from Harmonic Analysis\, in particular there is intimate connecti
 on with the BMO spaces.\nIf we have time we  will discuss also some new re
 sults in the context of multiparameter setting improving also some results
  from Shi-Torchinsky and\nLu-Wheeden from the 90's.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Carro (Universidad Complutense de Madrid)
DTSTART:20210218T144000Z
DTEND:20210218T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/17
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/17/">Boundedness of Bochner-Riesz operators on rearrangement inv
 ariant spaces</a>\nby María Carro (Universidad Complutense de Madrid) as 
 part of Function spaces\n\n\nAbstract\nWe shall present very briefly the B
 ochner-Riesz conjecture\, which is an open problem in dimension $n > 2$\, 
 and we shall prove\, with the help of the extrapolation theory of Rubio de
  Francia\, some estimates for the decreasing rearrangement of $B_\\alphaf$
 \, where $B_\\alpha$ is the B-R operator.\n\nAs a consequence\, we can giv
 e sufficient conditions (which are necessary sometimes) for the boundednes
 s of $B_\\alpha$ in weighted Lorentz spaces among other rearrangement inva
 riant spaces. \n\nThis is a joint work with Jorge Antezana\, Elona Agora a
 nd my PhD student Sergi Baena.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Soria (Universidad Complutense de Madrid)
DTSTART:20210225T144000Z
DTEND:20210225T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/18
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/18/">Optimal doubling measures and applications to graphs</a>\nb
 y Javier Soria (Universidad Complutense de Madrid) as part of Function spa
 ces\n\n\nAbstract\nIn a joint work with P. Tradacete\, we have recently pr
 oved that the doubling constant on any homogeneous metric measure space is
  at least 2. Continuing with this line of research\, and in collaboration 
 with E. Durand-Cartagena\, we have studied further results in the discrete
  case of graphs\, showing the connection between the optimal constant and 
 spectral properties.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Kristensen (University of Oxford)
DTSTART:20210304T144000Z
DTEND:20210304T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/19
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/19/">Regularity and uniqueness results in some variational probl
 ems</a>\nby Jan Kristensen (University of Oxford) as part of Function spac
 es\n\n\nAbstract\nIt is known that minimizers of strongly polyconvex varia
 tional integrals need not be regular nor unique. However\, if a suitable G
 årding type inequality is assumed for the variational integral\, then bot
 h regularity and uniqueness of minimizers can be restored under natural sm
 allness conditions on the data. In turn\, the Gårding inequality turns ou
 t to always hold under an a priori C1 regularity hypothesis on the minimiz
 er\, while its validity is not known in the general case. In this talk\, w
 e discuss these issues and how they are naturally connected to convexity o
 f the variational integral on the underlying Dirichlet classes.\n\nPart of
  the talk is based on ongoing joint work with Judith Campos Cordero\, Bern
 d Kirchheim and Jan Kolář\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nenad Teofanov (University of Novi Sad)
DTSTART:20210211T144000Z
DTEND:20210211T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/20
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/20/">Continuity properties of analytic pseudodifferential operat
 ors</a>\nby Nenad Teofanov (University of Novi Sad) as part of Function sp
 aces\n\n\nAbstract\nMotivated by some questions in quantum mechanics\, V. 
 Bargmann (in 1960s) introduced and studied integral transform that now bea
 rs his name. More recently\, J. Toft studied the mapping properties of the
  Bargmann transform when acting on Feichtinger’s modulation spaces. Thes
 e investigations served as a starting point in the recent study of analyti
 c pseudodifferential operators. Our aim is to give an introduction to rece
 nt results in that direction\, obtained with J. Toft and P. Wahlberg.\nIn 
 the first part of the talk\, we provide a historical background by discuss
 ing Hermite functions\, linear harmonic oscillator\, and different spaces 
 of (ultra)differentiable functions\, notably Pilipovic spaces. Thereafter\
 , we introduce the Bargmann transform and analytic pseudodifferential oper
 ators. To stress the connection with the classical theory\, we will consid
 er Wick and anti-Wick connection. At the end\, we briefly mention how our 
 findings can be used to recover and improve some known results in the cont
 ext of real analysis.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Kaltenbach (University of Freiburg)
DTSTART:20210311T144000Z
DTEND:20210311T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/21
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/21/">Variable exponent Bochner–Lebesgue spaces with symmetric 
 gradient structure</a>\nby Alex Kaltenbach (University of Freiburg) as par
 t of Function spaces\n\n\nAbstract\nWe introduce function spaces for the t
 reatment of non-linear parabolic equations with variable log-Hölder conti
 nuous exponents\, which only incorporate information of the symmetric part
  of a gradient. As an analogue of Korn’s inequality for these functions 
 spaces is not available\, the construction of an appropriate smoothing met
 hod proves itself to be difficult. To this end\, we prove a point-wise Poi
 ncaré inequality near the boundary of a bounded Lipschitz domain involvin
 g only the symmetric gradient. Using this inequality\, we construct a smoo
 thing operator with convenient properties. In particular\, this smoothing 
 operator leads to several density results\, and therefore to a generalized
  formula of integration by parts with respect to time. Using this formula 
 and the theory of maximal monotone operators\, we prove an abstract existe
 nce result.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Cobos (Universidad Complutense de Madrid)
DTSTART:20210415T134000Z
DTEND:20210415T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/22
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/22/">Interpolation of compact bilinear operators</a>\nby Fernand
 o Cobos (Universidad Complutense de Madrid) as part of Function spaces\n\n
 \nAbstract\nInterpolation of compact bilinear operators is a problem alrea
 dy considered by Calderón [2] in his foundational paper on the complex in
 terpolation method. The study on the real method started more recently wit
 h the papers by Fernadez and Silva [6] and Fernández-Cabrera and Martíne
 z [7\, 8]. An important motivation for this research has been the fact tha
 t compact bilinear operators occur rather naturally in harmonic analysis (
 see\, for example\, the paper by Bényi and Torres [1]).\n\nIn this talk\,
  we will review some recent results on the topic taken from joint papers w
 ith Fernández-Cabrera and Martínez [3\, 4\, 5].\n\n\n$\\text{\\large Ref
 erences}$\n\n$\\text{\n[1] Á.Bényi and R.H.Torres\, \\textit{Compact bil
 inear operators and commutator}\, Proc. Amer. Math. Soc. 141 (2013) 3609
 –3621.\n}$\n$\\text{\n[2] A.P. Calderón\, \\textit{Intermediate spaces 
 and interpolation\, the complex method}\, Studia Math. 24 (1964) 113–190
 .\n}$\n$\\text{\n[3] F. Cobos\, L.M. Fernández-Cabrera and A. Martínez\,
  \\textit{Interpolation of compact bilinear operators among quasi-Banach s
 paces and applications}\, Math. Nachr. 291 (2018) 2168–2187.\n}$\n$\\tex
 t{\n[4] F. Cobos\, L.M. Fernández-Cabrera and A. Martínez\, \\textit{On 
 compactness results of Lions-Peetre type for bilinear operators}\, Nonline
 ar Anal. 199 (2020) 111951.\n}$\n$\\text{\n[5] F. Cobos\, L.M. Fernández-
 Cabrera and A. Martínez\, \\textit{A compactness result of Janson type fo
 r bilinear operators}\, J. Math. Anal. Appl. 495 (2021) 124760.\n}$\n$\\te
 xt{\n[6] D.L. Fernandez and E.B. da Silva\, \\textit{Interpolation of bili
 near operators and compactness}\, Nonlinear Anal. 73 (2010) 526–537.\n}$
 \n$\\text{\n[7] L.M. Fernández-Cabrera and A. Martínez\, \\textit{On int
 erpolation properties of compact bilinear operators}\, Math. Nachr. 290 (2
 017) 1663–1677.\n}$\n$\\text{\n[8] L.M. Fernández-Cabrera and A. Martí
 nez\, \\textit{Real interpolation of compact bilinear operators}\, J. Four
 ier Anal. Appl. 24 (2018) 1181–1203.\n}$\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans G. Feichtinger (TU Wien and NuHAG)
DTSTART:20210318T144000Z
DTEND:20210318T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/23
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/23/">Completeness of sets of shifts in invariant Banach spaces o
 f functions</a>\nby Hans G. Feichtinger (TU Wien and NuHAG) as part of Fun
 ction spaces\n\n\nAbstract\nWe show that well-established methods from the
  theory of Banach modules and time-frequency analysis allow to derive comp
 leteness results for the collection of shifted and dilated version of a gi
 ven (test) function in a quite general setting. While the basic ideas show
  strong similarity to the arguments used in a recent paper by V. Katsnelso
 n we extend his results in several directions\, both relaxing the assumpti
 ons and widening the range of applications. There is no need for the Banac
 h spaces considered to be embedded into $(L^2(\\mathbb R)\, \\|\\cdot\\|_2
 )$\, nor is the Hilbert space structure relevant. We choose to present the
  results in the setting of the Euclidean spaces\, because then the Schwart
 z space $\\mathcal S'(\\mathbb R^d)$ $(d \\ge 1)$ of tempered distribution
 s provides a well-established environment for mathematical analysis. We al
 so establish connections to modulation spaces and Shubin classes $(Q_s(\\m
 athbb R^d)\, \\| \\cdot \\|_{Q_s} )$\, showing that they are special cases
  of Katsnelson’s setting (only) for $s \\ge 0$.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tino Ullrich (Technische Universität Chemnitz)
DTSTART:20210325T144000Z
DTEND:20210325T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/24
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/24/">Consequences of the Kadison Singer solution and Weaver's co
 njecture for the recovery of multivariate functions from a few random samp
 les</a>\nby Tino Ullrich (Technische Universität Chemnitz) as part of Fun
 ction spaces\n\n\nAbstract\nThe celebrated solution of the Kadison Singer 
 problem by Markus\, Spielman and Srivastava in 2015 via Weaver’s conject
 ure is the starting point for a new subsampling technique for finite frame
 s in $C^m$ by keeping the stability. We consider the special situation of 
 a frame coming from a finite orthonormal system of $m$ functions evaluated
  at random nodes (drawn from the orthogonality measure). It is well known 
 that this yields a good frame with high probability when we logarithmicall
 y oversample\, i.e. take $n$ samples with $n = m log(m)$. By the mentioned
  subsampling technique we may select a sub-frame of size $O(m)$. The conse
 quence is a new general upper bound for the minimal $L^2$-worst-case recov
 ery error in the framework of RKHS\, where only $n$ function samples are a
 llowed. This quantity can be bounded in terms of the singular numbers of t
 he compact embedding into the space of square-integrable functions. It tur
 ns out that in many relevant situations this quantity is asymptotically on
 ly worse by square root of $log(n)$ compared to the singular numbers. The 
 algorithm which realizes this behavior is a weighted least squares algorit
 hm based on a specific set of sampling nodes which works for the whole cla
 ss of functions simultaneously. These points are constructed out of a rand
 om draw with respect to distribution tailored to the spectral properties o
 f the reproducing kernel (importance sampling) in combination with a sub-s
 ampling mentioned above. For the above multivariate setting\, it is still 
 a fundamental open problem whether sampling algorithms are as powerful as 
 algorithms allowing general linear information like Fourier or wavelet coe
 fficients. However\, the gap is now rather small.\n\nThis is joint work wi
 th N. Nagel and M. Schaefer from TU Chemnitz.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Gibara (Université Laval\, Québec)
DTSTART:20210408T134000Z
DTEND:20210408T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/26
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/26/">The decreasing rearrangement and mean oscillation</a>\nby R
 yan Gibara (Université Laval\, Québec) as part of Function spaces\n\n\nA
 bstract\nIn joint work with Almut Burchard and Galia Dafni\, we study the 
 boundedness and continuity of the decreasing rearrangement on the space $\
 \operatorname{BMO}$ of functions of bounded mean oscillation in $\\mathbb{
 R}^n$. Improvements on the operator bounds will be presented\, including r
 ecent progress bringing the $O(2^{n/2})$ bound to $O(\\sqrt{n})$. Then\, t
 he failure of the continuity of decreasing rearrangement on $\\operatornam
 e{BMO}$ will be discussed\, along with some sufficient normalisation condi
 tions to guarantee continuity on the subspace $\\operatorname{VMO}$ of fun
 ctions of vanishing mean oscillation.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukáš Malý (Linköping University)
DTSTART:20210422T134000Z
DTEND:20210422T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/27
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/27/">Dirichlet problem for functions of least gradient in domain
 s with boundary of positive mean curvature in metric measure spaces</a>\nb
 y Lukáš Malý (Linköping University) as part of Function spaces\n\n\nAb
 stract\nSternberg\, Williams\, and Ziemer showed that the existence\, uniq
 ueness\, and regularity of solutions to the Dirichlet problem for $1$-Lapl
 acian on domains in $R^n$ are closely related to the mean curvature of the
  domain's boundary. In my talk\, I will discuss the problem of minimizatio
 n of the corresponding energy functional\, which can be naturally formulat
 ed and studied in the setting of $\\operatorname{BV}$ functions on metric 
 measure spaces. Having generalized the notion of positive mean curvature o
 f the boundary\, one can prove the existence of solutions to the Dirichlet
  problem. However\, solutions can fail to be continuous and/or unique even
  if the boundary and the boundary data are smooth\, which shall be demonst
 rated using fairly simple examples in weighted $R^2$.\n\nThe talk is based
  on joint work with Panu Lahti\, Nages Shanmugalingam\, and Gareth Speight
 \, with a contribution of Esti Durand-Cartagena and Marie Snipes.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Fernández Martínez (Universidad de Murcia)
DTSTART:20210401T134000Z
DTEND:20210401T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/28
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/28/">General Reiteration Theorems for $\\mathcal{R}$ and $\\math
 cal{L}$ spaces</a>\nby Pedro Fernández Martínez (Universidad de Murcia) 
 as part of Function spaces\n\n\nAbstract\nThe results contained in this le
 cture are part of an ongoing research project with T. Signes.  We will wor
 k with the real interpolation method defined by means of slowly varying fu
 nctions and rearrangement invariant (r.i.) spaces. More precisely\, for  $
 0 \\leq \\theta \\leq 1$\, $b$ a slowly varying function and $E$ an r.i. s
 pace we define the following interpolation space for the couple $\\overlin
 e{X} = (X_{0}\, X_{1})$:\n$$\n    \\overline{X}_{\\theta\,\\operatorname{b
 }\,E}=\\Big\\{f\\in X_0+X_1\\\;\\colon\\\;\n    \\big \\| t^{-\\theta} {\\
 operatorname{b}}(t) K(t\,f) \\big \\|_{\\widetilde{E}} < \\infty\\Big\\}.\
 n$$\nThis interpolation scale is stable under reiteration for $0 < \\theta
  <1$. Indeed\, for\n$0 <\\theta < 1$ and $0<\\theta_0<\\theta_1<1$\,\n$$\n
     \\big(  \\overline{X}_{\\theta_0\,\\operatorname{b}_0\,E_0}\, \\overli
 ne{X}_{\\theta_1\, \\operatorname{b}_{1}\, E_{1}} \\big)_{\\theta\, \\oper
 atorname{b}\, E}=\n    \\overline{X}_{\\tilde{\\theta}\,\\tilde{\\operator
 name{b}}\,E}.\n$$\nHowever\, interpolation with parameter $\\theta=0$ or $
 \\theta=1$ gives rise to the $\\mathcal{L}$ and $\\mathcal{R}$ spaces:\n$$
 \n    \\Big(  \\overline{X}_{\\theta_0\,\\operatorname{b}_0\,E_0}\, \\over
 line{X}_{\\theta_1\,\\operatorname{b}_1\,E_1}  \\Big)_{0\,\\operatorname{b
 }\,E}=\n    \\overline{X}^{\\mathcal{L}}_{\\theta_0\,\\operatorname{b}\\ci
 rc\\rho\,E\,\\operatorname{b}_0\,E_0}\n$$\n$$\n    \\Big( \\overline{X}_{\
 \theta_0\,\\operatorname{b}_0\,E_0}\, \\overline{X}_{\\theta_1\,\\operator
 name{b}_1\,E_1}\\Big)_{1\,\\operatorname{b}\,E}=\n    \\overline{X}^{\\mat
 hcal{R}}_{\\theta_1\,\\operatorname{b}\\circ\\rho\,E\,\\operatorname{b}_1\
 ,E_1}.\n$$\nHere\, we will present reiteration theorems that identify the 
 spaces\n$$\n    \\Big(\\overline{X}^{\\mathcal R}_{\\theta_0\,\\operatorna
 me{b}_0\,E_0\,a\,F}\, \\overline{X}_{\\theta_1\,\\operatorname{b}_1\,E_1}\
 \Big)_{\\theta\,\\operatorname{b}\,E}\n\\qquad\n    \\Big(\\overline{X}_{\
 \theta_0\,\\operatorname{b}_0\,E_0}\, \\overline{X}^{\\mathcal L}_{\\theta
 _1\, \\operatorname{b}_1\,E_1\,a\,F}\\Big)_{\\theta\,\\operatorname{b}\,E}
 \n$$\n$$\n    \\Big(\\overline{X}_{\\theta_0\,\\operatorname{b}_0\,E_0}\, 
 \\overline{X}^{\\mathcal R}_{\\theta_1\, \\operatorname{b}_1\,E_1\,a\,F}\\
 Big)_{\\theta\,\\operatorname{b}\,E}\n\\qquad\n    \\Big(\\overline{X}^{\\
 mathcal L}_{\\theta_0\, \\operatorname{b}_0\,E_0\,a\,F}\, \\overline{X}_{\
 \theta_1\,\\operatorname{b}_1\,E_1}\\Big)_{\\theta\,\\operatorname{b}\,E}.
 \n$$\n\nWe illustrate the use of these results with applications to interp
 olation of\ngrand and small Lebesgue spaces\, Gamma spaces and $A$ and $B$
 -type spaces.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gael Diebou Yomgne (University of Bonn)
DTSTART:20210429T134000Z
DTEND:20210429T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/29
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/29/">Stationary Navier-Stokes flow with irregular Dirichlet data
 </a>\nby Gael Diebou Yomgne (University of Bonn) as part of Function space
 s\n\n\nAbstract\nIn this talk\, we discuss recent results on the well-pose
 dness of the\nforced Navier-Stokes equations in bounded/unbounded domain (
 in arbitrary\ndimension) subject to Dirichlet data assuming minimal smooth
 ness\nproperties at the boundary. We will emphasize the construction of th
 e\nsolution space which reflects the intrinsic features (scaling and\ntran
 slation invariance\, type of nonlinearity) of the equation. Our\nmachinery
  together with some known facts in harmonic analysis and function\nspace t
 heory predicts a boundary class from a Triebel-Lizorkin scale. By\nprescri
 bing small data\, existence\, uniqueness\, and regularity results are\nobt
 ained using a non-variational approach. This solvability improves the\npre
 vious existing results which will be mentioned.\nIf time allows\, we will 
 also discuss the self-similarity properties of\nsolutions in a somewhat di
 fferent setting.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nages Shanmugalingam (University of Cincinnati)
DTSTART:20210513T134000Z
DTEND:20210513T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/30
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/30/">Uniformization of weighted Gromov hyperbolic spaces and uni
 formly locally bounded geometry</a>\nby Nages Shanmugalingam (University o
 f Cincinnati) as part of Function spaces\n\n\nAbstract\nThe seminal work o
 f Bourdon and Pajot gave a way of constructing a Gromov hyperbolic space w
 hose boundary is a compact doubling metric space of interest. The work of 
 Bonk\, Heinonen\, and Koskela gave us a way of turning a Gromov hyperbolic
  space into a uniform domain whose boundary is quasisymmetric to the origi
 nal compact doubling space. In this talk\, we will describe a way of unifo
 rmizing measures on a Gromov hyperbolic space that is uniformly locally do
 ubling and supports a uniformly local Poincare inequality to obtain a unif
 orm space that is equipped with a globally doubling measure supporting a g
 lobal Poincare inequality. This is then used to compare Besov spaces on th
 e original compact doubling space with traces of Newton-Sobolev spaces on 
 the uniform domain. This talk is based on joint work with Anders Bjorn and
  Jana Bjorn.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viktor Kolyada (Karlstad University)
DTSTART:20210520T134000Z
DTEND:20210520T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/31
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/31/">Estimates of Besov mixed-type norms for functions in Sobole
 v and Hardy-Sobolev spaces</a>\nby Viktor Kolyada (Karlstad University) as
  part of Function spaces\n\n\nAbstract\nWe prove embeddings of Sobolev and
  Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. Th
 is gives an improvement of the known embeddings into usual Besov spaces. A
 pplying these results\, we obtain Oberlin type estimates of Fourier transf
 orms for functions in Sobolev spaces.\n\nPublished in: Ann. Mat. Pura Appl
 .\, 192\, no. 2 (2019)\, 615-637.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petru Mironescu (l’Institut Camille Jordan de l’Université Ly
 on 1)
DTSTART:20210603T134000Z
DTEND:20210603T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/32
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/32/">Sobolev maps to the circle</a>\nby Petru Mironescu (l’Ins
 titut Camille Jordan de l’Université Lyon 1) as part of Function spaces
 \n\n\nAbstract\nSobolev spaces $W^{s\, p}$ of maps with values into a comp
 act manifold naturally appear in geometry and material sciences. They exhi
 bit qualitatively different properties from scalar Sobolev spaces: in gene
 ral\, there is no density of smooth maps\, and standard trace theory fails
 . We will present some of their basic properties\, with a focus on the cas
 es where $s<1$ or the target manifold is the circle\, in which harmonic an
 alysis tools combined with geometric considerations are quite effective. I
 n particular\, we discuss the factorization of unimodular maps\, which can
  be seen as a geometric version of paraproducts.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Maria Martell (ICMAT\, Madrid)
DTSTART:20210527T134000Z
DTEND:20210527T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/33
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/33/">Distilling Rubio de Francia's extrapolation theorem</a>\nby
  Jose Maria Martell (ICMAT\, Madrid) as part of Function spaces\n\n\nAbstr
 act\nRubio de Francia's extrapolation theorem states that if a given opera
 tor is bounded on $L^2(w)$ for all $w\\in A_2$\, then the same occurs on $
 L^p(w)$ for all $w\\in A_p$ and for all $p\\in(1\,\\infty)$. Its proof onl
 y uses the boundedness of the Hardy-Littlewood maximal function on weighte
 d spaces.  In this talk I will adopt a new viewpoint on which the desired 
 estimate follows from some "embedding" based on this basic ingredient. Thi
 s allows us to generalize extrapolation in the context of Banach function 
 spaces on which the some weighted estimates hold for the Hardy-Littlewood 
 maximal function.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polona Durcik (Chapman University)
DTSTART:20210617T134000Z
DTEND:20210617T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/34
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/34/">Singular Brascamp-Lieb inequalities with cubical structure<
 /a>\nby Polona Durcik (Chapman University) as part of Function spaces\n\n\
 nAbstract\nBrascamp-Lieb inequalities are Lp estimates for certain multili
 near integral forms on functions on Euclidean spaces. They generalize seve
 ral classical inequalities\, such as Hoelder's inequality or Young's convo
 lution inequality. In this talk\, we focus on singular Brascamp-Lieb inequ
 alities\, which arise when one of the functions in a Brascamp-Lieb integra
 l is replaced by a singular integral kernel. Singular Brascamp-Lieb integr
 als are much less understood than their non-singular variants. We discuss 
 some results and open problems in the area and focus on a special case whi
 ch features a particular cubical structure. Based on joint works with C. T
 hiele and work in progress with L. Slavíková and C. Thiele.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Van Schaftingen (Université catholique de Louvain)
DTSTART:20210701T134000Z
DTEND:20210701T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/35
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/35/">Estimates for the Hopf invariant in critical fractional Sob
 olev spaces</a>\nby Jean Van Schaftingen (Université catholique de Louvai
 n) as part of Function spaces\n\n\nAbstract\nThe Brouwer degree classifies
  the homotopy classes of mappings from a sphere into itself. Bourgain\, Br
 ezis and Mironescu have obtained some linear estimates of the degree of a 
 mapping by any critical first-order or fractional Sobolev energy. Similarl
 y\, maps from the three-dimensional sphere to the two-dimensional spheres 
 are classified by their Hopf invariant. Thanks to the Whitehead formula\, 
 Riviere has proved a sharp nonlinear control of the Hopf invariant by the 
 first-order critical Sobolev energy. I will explain how a general compactn
 ess argument implies that sets that have bounded critical fractional Sobol
 ev energy have bounded Hopf invariant and how we are obtaining in collabor
 ation with Armin Schikorra sharp nonlinear estimates in critical fractiona
 l Sobolev spaces with order is close to 1.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ritva Hurri-Syrjänen (University of Helsinki)
DTSTART:20210624T134000Z
DTEND:20210624T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/36
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/36/">On the John-Nirenberg space</a>\nby Ritva Hurri-Syrjänen (
 University of Helsinki) as part of Function spaces\n\n\nAbstract\nFritz Jo
 hn and Louis Nirenberg gave a summation condition for cubes\nwhich gives r
 ise to a function space. This $\\operatorname{JN}_p$ space has been less w
 ell\nknown than the $\\operatorname{BMO}$ space. The talk will address que
 stions related\nto functions belonging to the $\\operatorname{JN}_p$ space
  when the functions are defined\non certain domains in $R^n$.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Santeri Miihkinen (Karlstad University)
DTSTART:20210506T134000Z
DTEND:20210506T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/37
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/37/">The infinite Hilbert matrix on spaces of analytic functions
 </a>\nby Santeri Miihkinen (Karlstad University) as part of Function space
 s\n\n\nAbstract\nThe (finite) Hilbert matrix is arguably one of the single
  most well-known matrices in mathematics. The infinite Hilbert matrix $\\m
 athcal H$ was introduced by David Hilbert around 120 years ago in connecti
 on to his double series theorem. It can be interpreted as a linear operato
 r on spaces of analytic functions by its action on their Taylor coefficien
 ts. The boundedness of $\\mathcal H$ on the Hardy spaces $H^p$ for $1 < p 
 < \\infty$ and Bergman spaces $A^p$ for $2 < p < \\infty$ was established 
 by Diamantopoulos and Siskakis. The exact value of the operator norm of $\
 \mathcal H$ acting on the Bergman spaces $A^p$ for $4 \\le p < \\infty$ wa
 s shown to be $\\frac{\\pi}{\\sin(2\\pi/p)}$ by Dostanic\, Jevtic and Vuko
 tic in 2008. The case $2 < p < 4$ was an open problem until in 2018 it was
  shown by Bozin and Karapetrovic that the norm has the same value also on 
 the scale $2 < p < 4$. In this talk\, we review some of the old results an
 d consider the still partly open problem regarding the value of the norm o
 n weighted Bergman spaces. The talk is partly based on joint work with Mik
 ael Lindström and Niklas Wikman (Åbo Akademi).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianluigi Manzo (University of Naples)
DTSTART:20210610T134000Z
DTEND:20210610T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/38
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/38/">The spaces $BMO_{(s)}$ and o-O structures</a>\nby Gianluigi
  Manzo (University of Naples) as part of Function spaces\n\n\nAbstract\nIn
  2015 a new Banach space $B$ was introduced by Bourgain\, Brezis and Miron
 escu\, equipped with a norm defined as a supremum of oscillations. This sp
 ace has a subspace $B_0$ which has a vanishing condition the oscillations 
 and whose bidual is exactly $B$. This situation is similar to what happens
  with the $(VMO\,BMO)$: in fact\, there are many Banach spaces $E$\, defin
 ed by a supremum ("big o") condition that are biduals of a subspace $E_0$ 
 defined by a vanishing ("little o") condition. The space $B$ sparked the i
 nterest in these spaces\, with the help of a construction due to K. M. Per
 fekt. This talk aims to give a brief overview on some results on these o-O
  pairs\, with a focus on the family of spaces $BMO_{(s)}$ recently introdu
 ced by C. Sweezy.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loukas Grafakos (University of Missouri\, Columbia)
DTSTART:20220203T144000Z
DTEND:20220203T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/39
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/39/">From Fourier series to multilinear analysis</a>\nby Loukas 
 Grafakos (University of Missouri\, Columbia) as part of Function spaces\n\
 n\nAbstract\nWe present a survey of classical results related to summabili
 ty of Fourier series. We indicate how the question of summability of produ
 cts of Fourier series motivates the study of multilinear analysis\, in par
 ticular the study of multilinear multiplier problems. We discuss some new 
 results in this area and outline our methodology.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergi Baena Miret (University of Barcelona\, Spain)
DTSTART:20220210T144000Z
DTEND:20220210T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/40
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/40/">Decreasing rearrangements on average operators</a>\nby Serg
 i Baena Miret (University of Barcelona\, Spain) as part of Function spaces
 \n\n\nAbstract\nLet $\\{T_\\theta\\}_\\theta$ be a family of operators ind
 exed in a probability measure space $(\\Omega\, \\mathcal A\, P)$ such tha
 t the boundedness $$T_\\theta:L^1(u) \\longrightarrow  L^{1\, \\infty}(u)\
 , \\qquad \\forall u \\in A_1\,\n$$ holds with constant less than or equal
  to $\\varphi(\\lVert u \\rVert_{A_1})$\, with $\\varphi$ being a nondecre
 asing function on $(0\,\\infty)$ and where $A_1$ is the class of Muckenhou
 pt weights. The aim of this talk is to address the following two questions
 : what can we say about the  decreasing rearrangement of the average opera
 tor\n$$T_A f(x)= \\int_{\\Omega} T_\\theta f(x) dP(\\theta)\, \\qquad x \\
 in \\mathbb R^n\,$$ whenever is well defined and what can we say about its
  boundedness over r.i. spaces as\, for instance\, the classical Lorentz sp
 aces?\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Spector (National Taiwan Normal University)
DTSTART:20220217T144000Z
DTEND:20220217T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/41
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/41/">An Atomic Decomposition for Divergence Free Measures</a>\nb
 y Daniel Spector (National Taiwan Normal University) as part of Function s
 paces\n\n\nAbstract\nIn this talk\, we describe a recent result obtained i
 n collaboration with Felipe Hernandez where we give an atomic decompositio
 n for the space of divergence-free measures. The atoms in this setting are
  piecewise $C^1$ closed curves which satisfy a ball growth condition\, whi
 le our result can be used to deduce certain "forbidden" Sobolev inequaliti
 es which arise in the study of electricity and magnetism.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Rosario Mingione (Universita di Parma\, Italy)
DTSTART:20220224T144000Z
DTEND:20220224T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/42
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/42/">Perturbations beyond Schauder</a>\nby Giuseppe Rosario Ming
 ione (Universita di Parma\, Italy) as part of Function spaces\n\n\nAbstrac
 t\nSo-called Schauder estimates are a standard tool in the analysis of lin
 ear elliptic and parabolic PDEs. They had been originally proved by Hopf (
 1929\, interior case)\, and by Schauder and Caccioppoli (1934\, global est
 imates). Since then\, several proofs were given (Campanato\, Trudinger\, S
 imon). The nonlinear case is a more recent achievement from the 80s (Giaqu
 inta & Giusti\, Ivert\, J. Manfredi\, Lieberman). All these classical resu
 lts take place in the uniformly elliptic case. I will discuss progress in 
 the nonuniformly elliptic one. From joint work with Cristiana De Filippis.
 \n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Kh. Balci (Universität Bielefeld\, Germany)
DTSTART:20220324T144000Z
DTEND:20220324T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/43
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/43/">(Generalized) Sobolev-Orlicz Spaces of differential forms</
 a>\nby Anna Kh. Balci (Universität Bielefeld\, Germany) as part of Functi
 on spaces\n\n\nAbstract\nWe  study  generalised Sobolev-Orlicz spaces of d
 ifferential forms. In particular we provide results on density of smooth f
 unctions and design examples on Lavrentiev gap for partial spaces of diffe
 rential forms such as variable exponent\, double phase and weighted energy
 .  As an application we consider Lavrentiev gap for so-called borderline c
 ase of double phase potential model.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Karlovich (NOVA University Lisbon\, Portugal)
DTSTART:20211104T144000Z
DTEND:20211104T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/44
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/44/">On the interpolation constants for variable Lebesgue spaces
 </a>\nby Alexei Karlovich (NOVA University Lisbon\, Portugal) as part of F
 unction spaces\n\n\nAbstract\nFor $\\theta\\in(0\,1)$ and variable exponen
 ts $p_0(\\cdot)\,q_0(\\cdot)$ and\n$p_1(\\cdot)\,q_1(\\cdot)$ with values 
 in $[1\,\\infty]$\, let the variable exponents\n$p_\\theta(\\cdot)\,q_\\th
 eta(\\cdot)$ be defined by\n\\[\n1/p_\\theta(\\cdot):=(1-\\theta)/p_0(\\cd
 ot)+\\theta/p_1(\\cdot)\,\n\\quad\n1/q_\\theta(\\cdot):=(1-\\theta)/q_0(\\
 cdot)+\\theta/q_1(\\cdot).\n\\]\nThe Riesz-Thorin type interpolation theor
 em for variable Lebesgue spaces says\nthat if a linear operator $T$ acts b
 oundedly from the variable Lebesgue space\n$L^{p_j(\\cdot)}$ to the variab
 le Lebesgue space $L^{q_j(\\cdot)}$ for $j=0\,1$\,\nthen\n\\[\n\\|T\\|_{L^
 {p_\\theta(\\cdot)}\\to L^{q_\\theta(\\cdot)}}\n\\le\nC\n\\|T\\|_{L^{p_0(\
 \cdot)}\\to L^{q_0(\\cdot)}}^{1-\\theta}\n\\|T\\|_{L^{p_1(\\cdot)}\\to L^{
 q_1(\\cdot)}}^{\\theta}\,\n\\]\nwhere $C$ is an interpolation constant ind
 ependent of $T$. We consider two\ndifferent modulars $\\varrho^{\\max}(\\c
 dot)$ and $\\varrho^{\\rm sum}(\\cdot)$\ngenerating variable Lebesgue spac
 es and give upper estimates for the\ncorresponding interpolation constants
  $C_{\\rm max}$ and $C_{\\rm sum}$\,\nwhich imply that $C_{\\rm max}\\le 2
 $ and $C_{\\rm sum}\\le 4$\, as well as\, lead\nto sufficient conditions f
 or $C_{\\rm max}=1$ and $C_{\\rm sum}=1$. We also\nconstruct an example sh
 owing that\, in many cases\, our upper estimates are\nsharp and the interp
 olation constant is greater than one\, even if one requires\nthat $p_j(\\c
 dot)=q_j(\\cdot)$\, $j=0\,1$ are Lipschitz continuous and bounded\naway fr
 om one and infinity (in this case\n$\\varrho^{\\rm max}(\\cdot)=\\varrho^{
 \\rm sum}(\\cdot)$).\nThis is a joint work with Eugene Shargorodsky (King'
 s College London\, UK).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joao Pedro G. Ramos (ETH Zürich\, Switzerland)
DTSTART:20211111T144000Z
DTEND:20211111T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/45
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/45/">Stability for geometric and functional inequalities</a>\nby
  Joao Pedro G. Ramos (ETH Zürich\, Switzerland) as part of Function space
 s\n\n\nAbstract\nThe celebrated isoperimetric inequality states that\, for
  a measurable set $S \\subset \\R^n\,$ the inequality\n\\[\n\\text{per}(S)
  \\ge n \\text{vol}(S)^{\\frac{n-1}{n}} \\text{vol}(B_1)^{\\frac{1}{n}}\n\
 \]\nholds\, where $\\text{per}(S)$ denotes the perimeter (or surface area)
  of $S\,$ and equality holds if and only if $S$ is an euclidean ball. This
  result has many applications throughout analysis\, but an interesting fea
 ture is that it can be obtained as a corollary of a more general inequalit
 y\, the Brunn--Minkowski theorem: if $A\,B \\subset \\R^n\,$ define $A+B =
  \\{ a+b\, a \\in A\, b\\in B\\}.$ Then\n\\[\n|A+B|^{1/n} \\ge |A|^{1/n} +
  |B|^{1/n}.\n\\]\nHere\, equality holds if and only if $A$ and $B$ are hom
 othetic and convex. A question pertaining to both these results\, that aim
 s to exploit deeper features of the geometry behind them\, is that of stab
 ility: if $S$ is close to being optimal for the isoperimetric inequality\,
  can we say that $A$ is close to being a ball? Analogously\, if $A\,B$ are
  close to being optimal for Brunn--Minkowski\, can we say they are close t
 o being compact and convex?\n\nThese questions\, as stand\, have been answ
 ered only in very recent efforts by several mathematicians. In this talk\,
  we shall outline these results\, with focus on the following new result\,
  obtained jointly with A. Figalli and K. B\\"or\\"oczky. If $f\,g$ are two
  non-negative measurable functions on $\\R^n\,$ and $h:\\R^n \\to \\R_{\\g
 e 0}$ is measurable such that\n\\[\nh(x+y) \\ge f(2x)^{1/2} g(2y)^{1/2}\, 
 \\\, \\forall x\,y \\in \\R^n\,\n\\]\nthen the Prekopa--Leindler inequalit
 y asserts that\n\\[\n\\int h \\ge \\left(\\int f\\right)^{1/2} \\left( \\i
 nt g\\right)^{1/2}\,\n\\]\nwhere equality holds if and only if $h$ is log-
 concave\, and $f\,g$ are `homothetic' to $h$\, in a suitable sense. We pro
 ve that\, if $\\int h \\le (1+\\varepsilon) \\left(\\int f\\right)^{1/2} \
 \left( \\int g\\right)^{1/2}\,$ then $f\,g\,h$ are $\\varepsilon^{\\gamma_
 n}-$ $L^1-$close to being optimal. We will discuss the general idea for th
 e proof and\, time-allowing\, discuss on a conjectured sharper version.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iwona Chlebicka (Institute of Applied Mathematics and Mechanics\, 
 University of Warsaw\, Poland)
DTSTART:20211118T144000Z
DTEND:20211118T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/46
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/46/">Approximation properties of Musielak-Orlicz-Sobolev spaces 
 and its role in well-posedness of nonstandard growth PDE</a>\nby Iwona Chl
 ebicka (Institute of Applied Mathematics and Mechanics\, University of War
 saw\, Poland) as part of Function spaces\n\n\nAbstract\nMusielak-Orlicz-So
 bolev spaces describe in one framework Sobolev spaces with variable expone
 nt\, with double phase\, as well as isotropic and anisotropic Orlicz space
 s. There is significant interest in PDEs and calculus of variations fittin
 g in such a framework. These spaces share an essential difficulty - smooth
  functions are not dense in Musielak-Orlicz-Sobolev spaces unless the func
 tion generating them is regular enough. It is closely related to the so-ca
 lled Lavrentiev's phenomenon describing the situation when infima of a var
 iational functional over regular functions and over all functions in the e
 nergy space are different. Throughout the talk I will be explaining in det
 ail why for PDEs it is so critical to have density especially in non-refle
 xive spaces.\n\nThe typical examples of sufficient conditions for the dens
 ity is log-H\\"older continuity of the variable exponent or the closeness 
 condition for powers in the double phase spaces. Some sufficient condition
 s were known in the anisotropic cases\, but they were not truly capturing 
 full anisotropy. I will present new sufficient conditions obtained in coll
 aboration with Michał Borowski (student at University of Warsaw). They im
 prove previous conditions covering all known optimal conditions and being 
 essentially better than any non-doubling or anisotropic condition before.\
 n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Fraccaroli (University of Bonn\, Germany)
DTSTART:20211209T144000Z
DTEND:20211209T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/47
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/47/">Outer $L^p$ spaces: Köthe duality\, Minkowski inequality a
 nd more</a>\nby Marco Fraccaroli (University of Bonn\, Germany) as part of
  Function spaces\n\n\nAbstract\nThe theory of $L^p$ spaces for outer measu
 res\, or outer $L^p$ spaces\, was\ndeveloped by Do and Thiele to encode th
 e proof of boundedness of certain\nmultilinear operators in a streamlined 
 argument. Accordingly to this\npurpose\, the theory was developed in the d
 irection of the real\ninterpolation features of these spaces\, such as ver
 sions of H\\"{o}lder's\ninequality and Marcinkiewicz interpolation\, while
  other questions remained\nuntouched.\n\nFor example\, the outer $L^p$ spa
 ces are defined by quasi-norms\ngeneralizing the classical mixed $L^p$ nor
 ms on sets with a Cartesian\nproduct structure\; it is then natural to ask
  whether in arbitrary settings\nthe outer $L^p$ quasi-norms are equivalent
  to norms and what other\nreasonable properties they satisfy\, e.g. K\\"{o
 }the duality and Minkowski\ninequality. In this talk\, we will answer thes
 e questions\, with a\nparticular focus on two specific settings on the col
 lection of dyadic\nintervals in $\\mathbb{R}$ and the collection of dyadic
  Heisenberg boxes in\n$\\mathbb{R}^2$. This will allow us to clarify the r
 elation between outer\n$L^p$ spaces and tent spaces\, and get a glimpse at
  the use of this\nlanguage in the proof of boundedness of prototypical mul
 tilinear operators\nwith invariances.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Cameron Campbell (University of Hradec Králové)
DTSTART:20211216T144000Z
DTEND:20211216T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/48
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/48/">Closures of planar BV homeomorphisms and the relaxation of 
 functionals with linear growth</a>\nby Daniel Cameron Campbell (University
  of Hradec Králové) as part of Function spaces\n\n\nAbstract\nMotivated 
 by relaxation results of Kristensen and Rindler\, and of Benešová\, Krö
 mer and Kružík for BV maps\, we study the class of strict limits of BV p
 lanar homeomorphisms. We show that\, although such maps need not be inject
 ive and are not necessarily continuous on almost every line\, the class ha
 s a reasonable behavior expected for limit of elastic deformations. By a c
 haracterization of the classes of strict and area-strict limits of BV home
 omorphisms we show that these classes coincide.\n\nThis is based on joint 
 works with S. Hencl\, A. Kauranen and E. Radici.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franz Gmeineder (University of Konstanz\, Germany)
DTSTART:20220106T144000Z
DTEND:20220106T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/49
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/49/">A-quasiconvexity\, function spaces and regularity</a>\nby F
 ranz Gmeineder (University of Konstanz\, Germany) as part of Function spac
 es\n\n\nAbstract\nBy Morrey's foundational work\, quasiconvexity displays 
 a key\nnotion in the vectorial Calculus of Variations. A suitable generali
 sation\nthat keeps track of more elaborate differential conditions is give
 n by\nFonseca \\& Müller's $\\mathcal{A}$-quasiconvexity. With the topic 
 having\nfaced numerous contributions as to lower semicontinuity\, in this 
 talk I\ngive an overview of recent results for such problems with focus on
  the\nunderlying function spaces and the (partial) regularity of minima.\n
 \nThe talk is partially based on joint work with Sergio Conti (Bonn)\,\nLa
 rs Diening (Bielefeld)\, Bogdan Raita (Pisa) and Jean Van Schaftingen\n(Lo
 uvain).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Baroni (University of Parma\, Italy)
DTSTART:20220113T144000Z
DTEND:20220113T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/50
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/50/">New results for non-autonomous functionals with mild phase 
 transition</a>\nby Paolo Baroni (University of Parma\, Italy) as part of F
 unction spaces\n\n\nAbstract\nWe describe how different regularity assumpt
 ions on the x-dependence of the energy impact the regularity of minimizers
  of some non-autonomous functionals having nonuniform ellipticity of moder
 ate size. We put particular emphasis on double phase functionals with loga
 rithmic phase transition\, including some new results.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Pawlewicz (University of Warsaw\, Poland)
DTSTART:20220120T144000Z
DTEND:20220120T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/51
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/51/">On the Embedding of BV Space into Besov-Orlicz Space</a>\nb
 y Aleksander Pawlewicz (University of Warsaw\, Poland) as part of Function
  spaces\n\n\nAbstract\nDuring the presentation I will give a sufficient (a
 nd\, in the case of a compact domain\, necessary) condition for the bounde
 dness of the embedding operator from $BV(\\Omega)$ space (the space of int
 egrable functions for which a weak gradient exists and is a Radon measure)
  into Besov-Orlicz space $B_{\\varphi\,1}^\\psi(\\Omega)$\, where $\\Omega
 \\subseteq\\mathbb{R}^d$. The condition has a form of an integral inequali
 ty involving a Young function $\\varphi$ and a weight function $\\psi$ and
  can be written as follows \n\\[\n\\frac{s^{d-1}}{\\varphi^{-1}(s^d)}\\int
 _0^s\\frac{\\psi(1/t)}{t}dt + \\int_s^\\infty\\frac{\\psi(1/t)s^{d-1}}{\\v
 arphi^{-1}(ts^{d-1})t} dt < D\,\n\\]\nfor some constant $D>0$ and every $s
 >0$. The main tool of the proof will be the molecular decomposition of fun
 ctions from $BV$ space.\n\nThe talk will be based on a joint work with Mic
 hał Wojciechowski. Our paper "On the Embedding of BV Spaces into Besov-Or
 licz Space" is already available on arXiv.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincenzo Ferone (University of Naples Federico II\, Italy)
DTSTART:20220127T144000Z
DTEND:20220127T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/52
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/52/">Symmetrization for fractional elliptic problems: a direct a
 pproach</a>\nby Vincenzo Ferone (University of Naples Federico II\, Italy)
  as part of Function spaces\n\n\nAbstract\nWe provide new direct methods t
 o establish symmetrization results in the form of mass concentration (\\em
 ph{i.e.} integral) comparison for fractional elliptic equations of the typ
 e $(-\\Delta)^{s}u=f$ $(0 < s< 1 )$ in a bounded domain $\\Omega$\, equipp
 ed with homogeneous {Dirichlet }boundary conditions. The classical pointwi
 se Talenti rearrangement inequality is recovered in the limit $s\\rightarr
 ow1$. Finally\, explicit counterexamples constructed for all $s\\in(0\,1)$
  highlight that the same pointwise estimate cannot hold in a nonlocal sett
 ing\, thus showing the optimality of our results. This is a joint work wit
 h Bruno Volzone.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Hytönen (University of Helsinki)
DTSTART:20220310T144000Z
DTEND:20220310T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/53
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/53/">One-sided sparse domination</a>\nby Tuomas Hytönen (Univer
 sity of Helsinki) as part of Function spaces\n\n\nAbstract\nOver the past 
 ten years\, sparse domination has proven to be an efficient way to capture
  many key features of singular operators. Much of current research is abou
 t extending the method to ever more general classes of operators. The obje
 cts of this talk are somewhat against this trend: to dominate more specifi
 c operators\, but then to have these special features reflected in the est
 imates. More concretely\, we deal with ``one-sided" (or ``causal") operato
 rs such that $Tf(x)$ only depends on the function $f$ on one side of the p
 oint $x$. Is it then possible to obtain a sparse bound with the same kind 
 of causality? The dream theorem that one could hope for remains open\, but
  we are able to get a certain weaker version. This version is still good e
 nough to obtain the boundedness of one-sided operators in some function sp
 aces\, relevant for partial differential equations\, where usual "two-side
 d" operators are not bounded in general.\n\nThe talk is based on joint wor
 k with Andreas Rosén (https://arxiv.org/abs/2108.10597).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Raita (Scuola Normale Superiore\, Pisa\, Italy)
DTSTART:20220317T144000Z
DTEND:20220317T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/54
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/54/">Nonlinear spaces of functions and compensated compactness f
 or concentrations</a>\nby Bogdan Raita (Scuola Normale Superiore\, Pisa\, 
 Italy) as part of Function spaces\n\n\nAbstract\nWe study compensation phe
 nomena for fields satisfying both a pointwise\nand a linear differential c
 onstraint. The compensation effect takes the form of nonlinear\nelliptic e
 stimates\, where constraining the values of the field to lie in a cone com
 pensates\nfor the lack of ellipticity of the differential operator. We giv
 e a series of new examples of\nthis phenomenon\, focusing on the case wher
 e the cone is a subset of the space of symmetric matrices and the differen
 tial operator is the divergence or the curl. One of our main\nfindings is 
 that the maximal gain of integrability is tied to both the differential op
 erator\nand the cone\, contradicting in particular a recent conjecture fro
 m <a href='https://arxiv.org/abs/2106.03077'>arXiv:2106.03077</a>.\nThis a
 ppends the classical compensated compactness framework for oscillations wi
 th a\nvariant designed for concentrations\, and also extends the recent th
 eory of compensated\nintegrability due to D. Serre. In particular\, we fin
 d a new family of integrands that are\nDiv-quasiconcave under convex const
 raints\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Koch (Max Planck Institute Mathematics in the Sciences\, Lei
 pzig)
DTSTART:20220303T144000Z
DTEND:20220303T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/55
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/55/">Functionals with nonstandard growth and convex duality</a>\
 nby Lukas Koch (Max Planck Institute Mathematics in the Sciences\, Leipzig
 ) as part of Function spaces\n\n\nAbstract\nI will present recent results 
 obtained in collaboration with Jan Kristensen\n(Oxford) and Cristiana de F
 ilippis (Parma) concerning functionals of the\nform\n\\[\n\\min_{u\\in g+W
 ^{1\,p}_0 (\\Omega\,\\mathbb R^n)} \\int_{\\Omega}F(Du)\\\,dx\,\n\\]\nwher
 e $F(z)$ satisfies $(p\,q)$-growth conditions. In particular\, I will high
 light how ideas from convex duality theory can be used in order to show\n$
 L^1$-regularity of the stress $\\partial_z F(Du)$ and the validity of the 
 Euler--Lagrange\nequation without an upper growth bound on $F(x\,\\cdot)$ 
 as soon as $F(z)$ is convex\, proper\, essentially smooth and superlinear 
 in $z$. Further\, I will give a\nexample of how to use similar ideas to ob
 tain $W^{1\,q}$-regularity of minimisers\nunder controlled duality $(p\, q
 )$-growth with $2 \\le p \\le q \\le \\frac{np}{n-2}$.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Schwarzacher (University of Uppsala\, Sweden)
DTSTART:20220331T134000Z
DTEND:20220331T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/56
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/56/">Construction of a right inverse for the divergence in non-c
 ylindrical time dependent domains</a>\nby Sebastian Schwarzacher (Universi
 ty of Uppsala\, Sweden) as part of Function spaces\n\n\nAbstract\nWe discu
 ss the construction of a stable right inverse for the divergence operator 
 in non-cylindrical domains in space-time. The domains are assumed to be H
 ölder regular in space and evolve continuously in time. The inverse opera
 tor is of Bogovskij type\, meaning that it attains zero boundary values. W
 e provide estimates in Sobolev spaces of positive and negative order with 
 respect to both time and space variables. The regularity estimates on the 
 operator depend on the assumed Hölder regularity of the domain. The resul
 ts can naturally be connected to the known theory for Lipschitz domains. A
 s an application\, we prove refined pressure estimates for weak and very w
 eak solutions to Navier-Stokes equations in time-dependent domains. This i
 s a joint work with Olli Saari.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Hastö (University of Turku)
DTSTART:20220414T134000Z
DTEND:20220414T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/57
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/57/">Anisotropic generalized Orlicz spaces and PDE</a>\nby Peter
  Hastö (University of Turku) as part of Function spaces\n\n\nAbstract\nVe
 ctor-valued generalized Orlicz spaces can be divided into anisotropic\, qu
 asi-isotropic and isotropic. In isotropic spaces\, the Young function depe
 nds only on\nthe length of the vector\, i.e. $\\Phi(v)=\\phi(|v|)$. In the
  quasi-isotropic case $\\Phi(v)\\approx \\phi(v|)$ so the dependence is vi
 a the length of the vector up to a constant. In the anisotropic case\, the
 re is no such restriction\, and the Young function depends directly on the
  vector.\n\nBasic assumptions in anisotropic generalized Orlicz spaces are
  not as well understood as in the isotropic case. In this talk I explain t
 he assumptions and prove the equivalence of two widely used conditions in 
 the theory of generalized Orlicz spaces\, usually called (A1) and (M). Thi
 s provides a more natural and easily verifiable condition for use in the t
 heory of anisotropic generalized Orlicz spaces for results such as Jensen'
 s inequality.\n\nIn collaboration with Jihoon Ok\, we obtained maximal loc
 al regularity results of weak solutions or minimizers of\n\\[\n\\operatorn
 ame{div} A(x\, Du)=0\n\\quad\\text{and}\\quad\n\\min_u \\int_\\Omega F(x\,
 Du)\\\,dx\,\n\\]\nwhen $A$ or $F$ are general quasi-isotropic Young functi
 ons. In other words\, we studied the problem without recourse to special f
 unction structure and without\nassuming Uhlenbeck structure. We establishe
 d local $C^{1\,\\alpha}$-regularity for some $\\alpha\\in(0\,1)$ and $C^{\
 \alpha}$-regularity for any $\\alpha\\in(0\,1)$ of weak solutions and loca
 l minimizers. Previously known\, essentially optimal\, regularity results 
 are included as special cases.\n\nPreprints are available at https://www.p
 roblemsolving.fi/pp/.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Chang (Princeton University)
DTSTART:20220505T134000Z
DTEND:20220505T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/58
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/58/">Nikodym-type spherical maximal functions</a>\nby Alan Chang
  (Princeton University) as part of Function spaces\n\n\nAbstract\nWe study
  $L^p$ bounds on Nikodym maximal functions associated to spheres. In contr
 ast to the spherical maximal functions studied by Stein and Bourgain\, our
  maximal functions are uncentered: for each point in $\\mathbb R^n$\, we t
 ake the supremum over a family of spheres containing that point.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Ruzhansky (Ghent University\, Belgium)
DTSTART:20220421T134000Z
DTEND:20220421T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/60
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/60/">Subelliptic pseudo-differential calculus on compact Lie gro
 ups</a>\nby Michael Ruzhansky (Ghent University\, Belgium) as part of Func
 tion spaces\n\n\nAbstract\nIn this talk we will give an overview of severa
 l related pseudo-differential theories and give a comparison for them in t
 erms of regularity estimates\, on compact and nilpotent groups\, also cont
 rasting the cases of elliptic and sub elliptic classes in the compact case
 .\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert Frank (California Institute of Technology)
DTSTART:20220407T134000Z
DTEND:20220407T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/61
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/61/">Sobolev spaces and spectral asymptotics for commutators</a>
 \nby Rupert Frank (California Institute of Technology) as part of Function
  spaces\n\n\nAbstract\nWe discuss two different\, but related topics. The 
 first concerns a new\, derivative-free characterization of homogeneous\, f
 irst-order Sobolev spaces\, the second concerns spectral properties of so-
 called quantum derivatives\, which are commutators with a certain singular
  integral operator. At the endpoint\, these two topics come together and w
 e try to explain the analogy between the results and the proofs\, as well 
 as an open conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Óscar Domínguez (Université Claude Bernard Lyon 1)
DTSTART:20220428T134000Z
DTEND:20220428T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/62
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/62/">New estimates for the maximal functions and applications</a
 >\nby Óscar Domínguez (Université Claude Bernard Lyon 1) as part of Fun
 ction spaces\n\n\nAbstract\nWe discuss sharp pointwise inequalities for ma
 ximal operators\, in\nparticular\, an extension of DeVore’s inequality f
 or the moduli of\nsmoothness and a logarithmic variant of Bennett–DeVore
 –Sharpley’s\ninequality for rearrangements.\nThis is joint work with S
 ergey Tikhonov.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Glenn Byrenheid (Friedrich-Schiller University\, Jena (Germany))
DTSTART:20220519T134000Z
DTEND:20220519T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/63
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/63/">Sparse approximation for break of scale embeddings</a>\nby 
 Glenn Byrenheid (Friedrich-Schiller University\, Jena (Germany)) as part o
 f Function spaces\n\n\nAbstract\nWe study sparse approximation of Sobolev 
 type functions having dominating mixed smoothness regularity borrowed for 
 instance from the theory of solutions for the electronic Schrödinger equa
 tion. Our focus is on measuring approximation errors in the practically re
 levant energy norm. We compare the power of approximation for linear and n
 on-linear methods working on a dictionary of Daubechies wavelet functions.
  Explicit (non-)adaptive algorithms are derived that generate n-term appro
 ximants having dimension-independent rates of convergence.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angkana Rüland (Heidelberg University)
DTSTART:20220512T134000Z
DTEND:20220512T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/64
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/64/">On Rigidity\, Flexibility and Scaling Laws: The Tartar Squa
 re</a>\nby Angkana Rüland (Heidelberg University) as part of Function spa
 ces\n\n\nAbstract\nIn this talk I will discuss a dichotomy between rigidit
 y and flexibility for certain differential inclusions from materials scien
 ce and the role of function spaces in this dichotomy: While solutions in s
 ufficiently regular function spaces are ``rigid'' and are determined by th
 e ``characteristics'' of the underlying equations\, at low regularity this
  is lost and a plethora of ``wild'' irregular solutions exist. I will show
  that the scaling of certain energies could serve as a mechanism distingui
 shing these two regimes and may yield function spaces that separate these 
 regimes. By discussing the Tartar square\, I will present an example of a 
 situation with a dichotomy between rigidity and flexibility where such sca
 ling results can be proved.\n\nThis is based on joint work with Jamie Tayl
 or\, Antonio Tribuzio\, Christian Zillinger and Barbara Zwicknagl.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wentao Teng (Kwansei Gakuin University)
DTSTART:20220526T134000Z
DTEND:20220526T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/65
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/65/">Dunkl translations\, Dunkl--type $BMO$ space and Riesz tran
 sforms for Dunkl transform on $L^\\infty$</a>\nby Wentao Teng (Kwansei Gak
 uin University) as part of Function spaces\n\n\nAbstract\nWe study some re
 sults on the support of Dunkl translations on compactly supported function
 s. Then we will define Dunkl--type $BMO$ space and Riesz transforms for Du
 nkl transform on $L^\\infty$\, and prove the boundedness of Riesz transfor
 ms from $L^\\infty$ to Dunkl--type $BMO$ space under the uniform boundedne
 ss assumption of Dunkl translations. The proof and the definition in Dunkl
  setting will be harder than in the classical case for the lack of some si
 milar properties of Dunkl translations to that of classical translations. 
 We will also extend the preciseness of the description of support of Dunkl
  translations on characteristic functions by Gallardo and Rejeb to that on
  all nonnegative radial functions in $L^2(m_k)$.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olli Tapiola (Universitat Autònoma de Barcelona)
DTSTART:20221013T134000Z
DTEND:20221013T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/66
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/66/">John conditions\, Harnack chains and boundary Poincaré ine
 qualities</a>\nby Olli Tapiola (Universitat Autònoma de Barcelona) as par
 t of Function spaces\n\n\nAbstract\nWe consider connections between the lo
 cal John condition\, the Harnack chain condition and weak boundary Poincar
 é inequalities in an open set $\\Omega \\subset \\mathbb{R}^{n+1}$ with $
 n$-dimensional Ahlfors--David regular boundary. First\, we show that if $\
 \Omega$ satisfies both the local John condition and the exterior corkscrew
  condition\, then $\\Omega$ also satisfies the Harnack chain condition (an
 d hence\, is a chord-arc domain). Second\, we show that if $\\Omega$ is a 
 2-sided chord-arc domain\, then the boundary $\\partial \\Omega$ supports 
 a Heinonen--Koskela-type weak $p$-Poincaré inequality for any $1 \\le p <
  \\infty$. We also discuss the optimality of our assumptions and some foll
 ow-up questions. This is a joint work with Xavier Tolsa.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marvin Weidner (Universitat de Barcelona)
DTSTART:20221027T134000Z
DTEND:20221027T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/67
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/67/">Regularity for nonlocal problems with non-standard growth</
 a>\nby Marvin Weidner (Universitat de Barcelona) as part of Function space
 s\n\n\nAbstract\nIn this talk\, we study robust regularity estimates for l
 ocal minimizers of nonlocal functionals with non-standard growth of (p\,q)
 -type. Our main focus is on Hölder regularity estimates and full Harnack 
 inequalities. Moreover\, our results apply to weak solutions to a related 
 class of nonlocal equations. This talk is based on joint works with Jamil 
 Chaker and Minhyun Kim.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michał Borowski (University of Warsaw)
DTSTART:20221110T144000Z
DTEND:20221110T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/68
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/68/">Boundedness of Wolff-type potentials</a>\nby Michał Borows
 ki (University of Warsaw) as part of Function spaces\n\n\nAbstract\nWe stu
 dy the boundedness of nonlinear operators of Wolff-type in a generalized v
 ersion. The main result is an optimal inequality on the rearrangement of m
 entioned operators\, which allows us to formulate the reduction principle 
 of boundedness between quasi-normed rearrangement invariant spaces into a 
 one-dimensional Hardy-type inequality. The principle can be extended to ha
 ndle modulars instead of norms. As Wolff-type potentials are known to cont
 rol weak solutions to a broad class of quasilinear elliptic PDEs\, we infe
 r regularity properties of the solutions to appropriate problems. The talk
  is based on joint work with Iwona Chlebicka and Błażej Miasojedow.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vjekoslav Kovač (University of Zagreb)
DTSTART:20221020T134000Z
DTEND:20221020T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/69
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/69/">Bilinear and trilinear embeddings for complex elliptic oper
 ators</a>\nby Vjekoslav Kovač (University of Zagreb) as part of Function 
 spaces\n\n\nAbstract\nWe will discuss bi(sub)linear and tri(sub)linear emb
 eddings for semigroups generated by non-smooth complex-coefficient ellipti
 c operators in divergence form. Bilinear embeddings can be thought of as s
 harpenings and generalizations of estimates for second-order singular inte
 grals. In the context of complex elliptic operators such $L^p$ bounds were
  shown by Carbonaro and Dragičević\, who emphasized and crucially used c
 ertain generalized convexity properties of powers. We remove this obstruct
 ion and generalize their approach to the level of Orlicz-space norms that 
 only “behave like powers”. Next\, what we call a trilinear embedding i
 s a paraproduct-type estimate. It incorporates bounds for the conical squa
 re function and finds an application to fractional Leibniz-type rules. In 
 the proofs we use two carefully constructed auxiliary functions that gener
 alize a classic Bellman function constructed by Nazarov and Treil in two d
 ifferent ways. The talk is based on joint work with Andrea Carbonaro\, Oli
 ver Dragičević\, and Kristina Škreb.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Odí Soler i Gibert (University of Würzburg)
DTSTART:20221103T144000Z
DTEND:20221103T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/70
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/70/">Dyadic multiparameter $\\mathrm{BMO}$ spaces</a>\nby Odí S
 oler i Gibert (University of Würzburg) as part of Function spaces\n\n\nAb
 stract\nWe will review some properties of the classical $\\mathrm{BMO}$ sp
 ace. In particular\, we will focus on commutators of the form $[H\,b]\,$ w
 here $b$ stands for multiplication by function $b$ in $\\mathrm{BMO}$ and 
 $H$ is the Hilbert transform\, and the equivalence between the norm of $[H
 \,b]$ (as an operator in $\\mathrm{L}^2$) and the $\\mathrm{BMO}$ norm of 
 $b.$ Then\, we will discuss similar results in various generalisations of 
 BMO: weighted spaces and multiparameter spaces. Lastly\, we will present t
 he corresponding dyadic spaces and how to obtain analogous results in this
  setting. This talk is based on joint works with Komla Domelevo\, Spyridon
  Kakaroumpas and Stefanie Petermichl.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioannis Parissis (University of the Basque Country)
DTSTART:20221124T144000Z
DTEND:20221124T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/71
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/71/">Directional averages in codimension one</a>\nby Ioannis Par
 issis (University of the Basque Country) as part of Function spaces\n\n\nA
 bstract\nI will give a brief overview of the theory of directional maximal
  and singular averages and describe the connection to the Kakeya/Nikodym l
 ine of problems. For general ambient dimension n I will then discuss a sha
 rp L^2-bound for d-dimensional averages and codimension n-d=1\, together w
 ith consequences for directional square functions of Rubio de Francia type
 . If time permits I will mention sharp L^2-bounds for general codimension 
 and a corresponding (d\,n)-Nikodym conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Nieraeth (Basque Center for Applied Mathematics)
DTSTART:20221215T144000Z
DTEND:20221215T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/72
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/72/">Extrapolation in quasi-Banach function spaces</a>\nby Zoe N
 ieraeth (Basque Center for Applied Mathematics) as part of Function spaces
 \n\n\nAbstract\nRubio de Francia's extrapolation theorem allows one to sho
 w that an operator that is bounded on weighted Lebesgue spaces for a singl
 e exponent and with respect to all weights in the associated Muckenhoupt c
 lass has to also be bounded for every exponent. As a matter of fact\, in t
 he previous years it has been shown that the operator has to be bounded on
  a much larger class of spaces\, including Lorentz\, variable Lebesgue\, a
 nd Morrey spaces\, and further weighted Banach function spaces. In this ta
 lk I will discuss a recently obtained unification and extension of some of
  these results by presenting an extrapolation theorem in the setting of ge
 neral quasi-Banach function spaces\, including limited range and off-diago
 nal variants.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bae Jun Park (Sungkyunkwan University)
DTSTART:20221222T144000Z
DTEND:20221222T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/73
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/73/">Equivalences of (quasi-)norms in a certain vector-valued fu
 nction space and its applications to multilinear operators</a>\nby Bae Jun
  Park (Sungkyunkwan University) as part of Function spaces\n\n\nAbstract\n
 In this talk we will study some  (quasi-)norm equivalences\, involving $L^
 p(\\ell^q)$ norm\, in a certain vector-valued function space and extend th
 e equivalences to $p=\\infty$ and $0 < q < \\infty$ in the scale of Triebe
 l-Lizorkin spaces. As an immediate consequence of our results\, $\\Vert f\
 \Vert_{BMO}$ can be written as $L^{\\infty}(\\ell^2)$ norm of a variant of
  $f$.\nWe will also discuss some applications to  multilinear operators.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Błażej Wróbel (University of Wrocław)
DTSTART:20230504T134000Z
DTEND:20230504T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/74
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/74/">Dimension-free $L^p$ estimates for the vector of maximal Ri
 esz transforms</a>\nby Błażej Wróbel (University of Wrocław) as part o
 f Function spaces\n\n\nAbstract\nIn 1983 E. M. Stein proved that the vecto
 r of classical Riesz transforms has $L^p$ bounds on $\\mathbb R^d$ which a
 re independent of the dimension. I will discuss an analogous result for th
 e vector of maximal Riesz transforms. I will also mention generalizations 
 to higher order Riesz transforms. The talk is based on recent joint work w
 ith Maciej Kucharski and Jacek Zienkiewicz (Wrocław).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cody B. Stockdale (Clemson University)
DTSTART:20230216T144000Z
DTEND:20230216T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/75
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/75/">A different approach to endpoint weak-type estimates for Ca
 lderón-Zygmund operators</a>\nby Cody B. Stockdale (Clemson University) a
 s part of Function spaces\n\n\nAbstract\nThe weak-type (1\,1) estimate for
  Calderón-Zygmund operators is fundamental in harmonic analysis. We inves
 tigate weak-type inequalities for Calderón-Zygmund singular integral oper
 ators using the Calderón-Zygmund decomposition and ideas inspired by Naza
 rov\, Treil\, and Volberg. We discuss applications of these techniques in 
 the Euclidean setting\, in weighted settings\, for multilinear operators\,
  for operators with weakened smoothness assumptions\, and in studying the 
 dimensional dependence of the Riesz transforms.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tainara Borges (Brown University)
DTSTART:20230316T144000Z
DTEND:20230316T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/76
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/76/">$L^p$ improving continuity estimates and sparse bounds for 
 the bilinear spherical maximal function</a>\nby Tainara Borges (Brown Univ
 ersity) as part of Function spaces\n\n\nAbstract\nIn this talk\, I will ex
 plain the interplay between the sharp range of\nparameters for each one ha
 s sparse domination for certain spherical maximal\nfunctions and the sharp
  $L^p$\nimproving boundedness region of corresponding\nlocalized spherical
  maximal operators\, an idea that was first exploited in a\nwork of M. Lac
 ey. I will then talk about joint work with B. Foster\, Y. Ou\,\nJ. Pipher\
 , and Z. Zhou\, in which we proved sparse domination results for a\nbiline
 ar generalization of the spherical maximal function in any dimension\n$d \
 \geq 2$\, and in dimension $1$ for its lacunary version. Such sparse domin
 ation\nresults allow one to recover the known sharp $L^p \\times L^q \\rig
 htarrow L^r$ bounds for the\nbilinear spherical maximal operator and to de
 duce new quantitative weighted\nnorm inequalities with respect to bilinear
  Muckenhoupt weights.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luz Roncal (BCAM Bilbao)
DTSTART:20230223T144000Z
DTEND:20230223T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/77
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/77/">Singular integrals along variable codimension one subspaces
 </a>\nby Luz Roncal (BCAM Bilbao) as part of Function spaces\n\n\nAbstract
 \nIn this talk we will consider maximal operators on $\\mathbb{R}^n$ forme
 d by taking arbitrary rotations of tensor products of a $n-1$-dimensional 
 Hörmander--Mihlin multiplier with the identity in 1 coordinate. These max
 imal operators are naturally connected to differentiation problems and max
 imally modulated singular integrals such as Sjölin's generalization of Ca
 rleson's maximal operator. Our main result is a weak-type $L^{2}(\\mathbb{
 R}^n)$-estimate  on band-limited functions. As corollaries\, we obtain: \n
 \n1. A sharp $L^2(\\mathbb{R}^n)$ estimate for the maximal operator restri
 cted to a finite set of rotations in terms of the cardinality of the finit
 e set. \n\n2. A version of the Carleson-Sjölin theorem. \n\nIn addition\,
  we obtain that functions in the Besov space $B_{p\,1}^0(\\mathbb{R}^n)$\,
  $2\\le p <\\infty$\, may be recovered from their averages along a measura
 ble choice of codimension $1$ subspaces\, a form of the so-called Zygmund'
 s conjecture in general dimension $n$.\n\nThis is joint work with Odysseas
  Bakas\, Francesco Di Plinio\, and Ioannis Parissis.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Nowak (Bielefeld University)
DTSTART:20230302T144000Z
DTEND:20230302T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/78
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/78/">Nonlocal gradient potential estimates</a>\nby Simon Nowak (
 Bielefeld University) as part of Function spaces\n\n\nAbstract\nWe conside
 r nonlocal equations of order larger than one with measure data and presen
 t pointwise bounds of the gradient in terms of Riesz potentials. These gra
 dient potential estimates lead to fine regularity results in many commonly
  used function spaces\, in the sense that "passing through potentials" ena
 bles us to detect finer scales that are difficult to reach by more traditi
 onal methods.\nThe talk is based on joint work with Tuomo Kuusi and Yannic
 k Sire.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armin Schikorra (University of Pittsburgh)
DTSTART:20230323T144000Z
DTEND:20230323T154000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/79
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/79/">A Harmonic Analysis perspective on $W^{s\,p}$ as $s \\to 1^
 -$</a>\nby Armin Schikorra (University of Pittsburgh) as part of Function 
 spaces\n\n\nAbstract\nWe revisit the Bourgain-Brezis-Mironescu result that
  the\nGagliardo-Norm of the fractional Sobolev space W^{s\,p}\, up to\nres
 caling\, converges to W^{1\,p} as s\\to 1.\nWe do so from the perspective 
 of Triebel-Lizorkin spaces\, by finding\nsharp $s$-dependencies for severa
 l embeddings between $W^{s\,p}$ and\n$F^{s\,p}_q$ where $q$ is either 2 or
  $p$.\nWe recover known results\, find a few new estimates\, and discuss s
 ome\nopen questions.\nJoint work with Denis Brazke\, Po-Lam Yung.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olli Saari (Universitat Politècnica de Catalunya)
DTSTART:20230406T134000Z
DTEND:20230406T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/80
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/80/">Construction of a phase space localizing operator</a>\nby O
 lli Saari (Universitat Politècnica de Catalunya) as part of Function spac
 es\n\n\nAbstract\nA partition into tiles of the area covered by a convex t
 ree in the Walsh phase plane gives an orthonormal basis for a subspace of 
 L2. There exists a related projection operator\, which has been an importa
 nt tool for dyadic models of the bilinear Hilbert transform. Extending suc
 h an approach to the Fourier model is strictly speaking not possible\, but
  satisfactory substitutes can be constructed. This approach was pursued by
  Muscalu\, Tao and Thiele (2002) for proving uniform bounds for multilinea
 r singular integrals with modulation symmetry in dimension one. I discuss 
 a multidimensional variant of the problem. This is based on joint work wit
 h Marco Fraccaroli and Christoph Thiele.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Olivo (ICTP Trieste)
DTSTART:20230413T134000Z
DTEND:20230413T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/81
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/81/">About the decay of the Fourier transform of self-similar me
 asures on the complex plane</a>\nby Andrea Olivo (ICTP Trieste) as part of
  Function spaces\n\n\nAbstract\nIn this talk we are going to discuss about
  the behaviour of self-similar\nmeasures and its Fourier transform. It is 
 known that\, in some particular\ncases\, the Fourier transform of a self-s
 imilar measure does not go zero\nwhen the frequencies goes to infinity. Ne
 vertheless\, Kaufman and Tsujii\nproved that the Fourier transform of self
 -similar measures on the real\nline has a power decay outside of a sparse 
 set of frequencies. We will go\nover these results and present a version f
 or homogeneous self-similar\nmeasures on the complex plane.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolin Kreisbeck (KU Eichstätt-Ingolstadt)
DTSTART:20230427T134000Z
DTEND:20230427T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/82
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/82/">A variational theory for integral functionals involving fin
 ite-horizon fractional gradients</a>\nby Carolin Kreisbeck (KU Eichstätt-
 Ingolstadt) as part of Function spaces\n\n\nAbstract\nMotivated by new non
 local models in hyperelasticity\, we discuss a class of variational proble
 ms with integral functionals depending on nonlocal gradients that correspo
 nd to truncated versions of the Riesz fractional gradient. We address seve
 ral aspects regarding the existence theory of these problems and their asy
 mptotic behavior. Our analysis relies on suitable translation operators th
 at allow us to switch between the three types of gradients: classical\, fr
 actional\, and nonlocal. These provide helpful technical tools for transfe
 rring results from one setting to the other. Based on this approach\, we s
 how that quasiconvexity\, the natural convexity notion in the classical ca
 lculus of variations\, characterises the weak lower semicontinuity also in
  the fractional and nonlocal setting. As a consequence of a general Gamma-
 convergence statement\, we derive relaxation and homogenization results. T
 he analysis of the limiting behavior as the fractional order tends to 1 yi
 elds localization to a classical model. This is joint work with Javier Cue
 to (University of Nebraska-Lincoln) and Hidde Schönberger (KU Eichstätt-
 Ingolstadt).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Irving (Technical University of Dortmund)
DTSTART:20230330T134000Z
DTEND:20230330T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/83
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/83/">Fractional differentiability and (p\,q)-growth</a>\nby Chri
 stopher Irving (Technical University of Dortmund) as part of Function spac
 es\n\n\nAbstract\nI will discuss some recent regularity results obtained f
 or minimisers of non-autonomous variational integrals\, with an emphasis t
 owards boundary regularity. We will consider integrands which are non-unif
 ormly elliptic in the sense that they satisfy a natural $(p\,q)$-growth co
 ndition\, and we will seek improved differentiability in fractional scales
 . The main ideas will be illustrated in the interior case\, and some exten
 sions to the boundary will be discussed. The results presented have been o
 btained jointly with Lukas Koch (MPI Lepzig).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasios Fragkos (Washington University in St. Louis)
DTSTART:20230420T134000Z
DTEND:20230420T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/84
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/84/">Modulation Invariant Operators near $L^1$</a>\nby Anastasio
 s Fragkos (Washington University in St. Louis) as part of Function spaces\
 n\n\nAbstract\nWe prove that the weak-$L^{p}$ norms\, and in fact the spar
 se $(p\,1)$-norms\, of the Carleson maximal partial Fourier sum operator a
 re $\\lesssim (p-1)^{-1}$ as $p\\to 1^+$. Furthermore\, our sparse $(p\,1)
 $-norms bound imply new and stronger results at the endpoint $p=1$. In par
 ticular\, we obtain that the Fourier series of functions from the weighted
  Arias de Reyna space $ \\mathrm{QA}_{\\infty}(w) $\, which contains the w
 eighted Antonov space $L\\log L\\log\\log\\log L(\\mathbb T\; w)$\, conver
 ge almost everywhere whenever $w\\in A_1$. This is an extension of the res
 ults of Antonov and Arias De Reyna\, where $w$ must be Lebesgue measure.\n
 \nThe center of our approach is a sharply quantified near-$L^1$ Carleson e
 mbedding theorem for the modulation-invariant wave packet transform. The p
 roof of the Carleson embedding is based on a newly developed smooth multi-
 frequency decomposition which\, near the endpoint $p=1$\, outperforms the 
 abstract Hilbert space approach of past works\, including the seminal one 
 by Nazarov\, Oberlin and Thiele. This talk is based on joint work with Fra
 ncesco Di Plinio.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Weigt (University of Warwick)
DTSTART:20230518T134000Z
DTEND:20230518T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/85
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/85/">Endpoint regularity bounds of maximal operators in higher d
 imensions</a>\nby Julian Weigt (University of Warwick) as part of Function
  spaces\n\n\nAbstract\nWe prove the endpoint regularity bound that the var
 iation of various maximal functions is bounded by a constant times the var
 iation of the function in any dimension.\n\nThe key arguments of the proof
 s are of geometric nature. For example new variants of the isoperimetric i
 nequality and of the Vitali covering lemma are proven and used. All proofs
  are mostly elementary up to applications of classical results like the re
 lative isoperimetric inequality and the coarea formula and approximation s
 chemes.\n\nSome of the arguments only work for cubes and not for balls. Th
 us\, for the uncentered Hardy-Littlewood maximal operator we can only prov
 e the above endpoint Sobolev bound in the case of characteristic functions
 . However\, we are able to prove it for general functions for example for 
 the maximal operator that averages over uncentered cubes with any orientat
 ion instead of balls. The methods also enable a proof of the corresponding
  endpoint bound Sobolev for the fractional centered and uncentered Hardy-L
 ittlewood maximal functions.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Sauer (Friedrich Schiller University Jena)
DTSTART:20230511T134000Z
DTEND:20230511T144000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/86
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/86/">General Time-Periodic Boundary Value Problems in Weighted S
 paces</a>\nby Jonas Sauer (Friedrich Schiller University Jena) as part of 
 Function spaces\n\n\nAbstract\nInbetween elliptic PDEs\, which do not depe
 nd on time (think of the steady-state Stokes equations)\,\nand honest para
 bolic PDEs\, which do depend on time and are started at a given initial va
 lue (think\nof the instationary Stokes equations)\, there are time-periodi
 c parabolic PDEs: On the one hand\,\ntime-independent solutions to the ell
 iptic PDE are also trivially time-periodic\, which gives periodic\nproblem
 s an elliptic touch\, on the other hand solutions to the initial value pro
 blem which are not\nconstant in time might very well be periodic.\n\nI wan
 t to advocate for time-periodic problems not being the little sister of ei
 ther elliptic or\nparabolic problems\, but being a connector between the t
 wo and a class of its own right. This is\nhighlighted by a direct method f
 or showing a priori $L^p$\nestimates for time-periodic\, linear\, partial\
 ndifferential equations. The method is generic and can be applied to a wid
 e range of problems\, for\nexample the Stokes equations and boundary value
  problems of Agmon-Douglas-Nirenberg type. In\nthe talk\, I will present t
 hese ideas and show how they can be extended to the setting of weighted\n$
 L^p$\nestimates\, which is advantageous for extrapolation techniques and r
 ougher boundary data.\n\nParts of the talk are based on joint works with Y
 asunori Maekawa and Mads Kyed.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jehoon Ok (Sogang University\, South Korea)
DTSTART:20231024T120000Z
DTEND:20231024T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/87
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/87/">Everywhere and partial regularity for parabolic systems wit
 h general growth</a>\nby Jehoon Ok (Sogang University\, South Korea) as pa
 rt of Function spaces\n\n\nAbstract\nWe discuss on regularity theory for p
 arabolic systems of the form\n\n$$\n\nu_t - \\mathrm{div} A(Du) =0 \\quad 
 \\text{in }\\ \\Omega_T=\\Omega\\times(0\,T]\,\n\n$$\n\nwhere $u:\\Omega_T
 \\to \\mathbb{R}^N$\, $u=u(x\,t)$\, is a vector valued function and the no
 nlinearity $A:\\mathbb{R}^{nN}\\to \\mathbb{R}^{nN}$ satisfies a general O
 rlicz growth condition characterized by exponents $p$ and $q$\, subject to
  the inequality $\\frac{2n}{n+2}<p<q$. It is noteworthy that when if $p<2<
 q$\, the degeneracy of the system remains indeterminate. \n\n\n\nThis talk
  focuses on presenting my recent developments in the realm of regularity r
 esults concerning  the spatial gradient $Du$ of solutions of the above sys
 tem\, which include the higher higher integrability of $Du$\, H\\"older co
 ntinuity of $Du$ when $A(\\xi)$ satisfies the Uhlenbeck structure\, i.e.\,
  $A(\\xi)=\\frac{\\varphi'(|\\xi|)}{|\\xi|}\\xi$\, and partial H\\"older c
 ontinuity of $Du$. These results are joint works with Giovanni Scilla and 
 Bianca Stroffolini from University of Naples\, Federico II\, and Peter H\\
 "ast\\"o from University of Turku.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Weimar (Die Julius-Maximilians-Universität Würzburg)
DTSTART:20231010T120000Z
DTEND:20231010T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/88
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/88/">Theory of Function Spaces: On Classical Tools for Modern Sp
 aces</a>\nby Markus Weimar (Die Julius-Maximilians-Universität Würzburg)
  as part of Function spaces\n\n\nAbstract\nIn the first part of this talk\
 , we discuss basic principles of the theory of function spaces. In particu
 lar\, we briefly recall the Fourier analytical approach towards classical 
 smoothness spaces of distributions and point out their importance in the a
 reas of approximation theory and the regularity theory of PDEs.\n\nThe mai
 n part of the talk is devoted to so-called Triebel-Lizorkin-Morrey spaces 
 $\\mathcal{E}_{u\,p\,q}^s$ of positive smoothness $s$ which attracted some
  attention in the last 15 years. This family of function spaces generalize
 s the by now well-established scale of Triebel-Lizorkin spaces $F^s_{p\,q}
 $ which particularly contains the usual $L_p$-Sobolev spaces $H^s_p=F^s_{p
 \,2}$ as special cases. Moreover\, there are strong relations to standard 
 classes of functions like BMO and Campanato spaces which are widely used i
 n the analysis of PDEs.\nWe will present new characterizations of Triebel-
 Lizorkin-Morrey spaces in terms of classical tools such as local oscillati
 ons (i.e.\, local polynomial bestapproximations) as well as ball means of 
 higher order differences. Hence\, under standard assumptions on the parame
 ters involved\, we extend assertions due to Triebel 1992 and Yuan/Sickel/Y
 ang 2010 for spaces $\\mathcal{E}_{u\,p\,q}^s$ on $\\mathbb{R}^d$ and addi
 tionally consider their restrictions to (bounded) Lipschitz domains $\\Ome
 ga\\subseteq \\mathbb{R}^d$. \nIf time permits\, we moreover indicate poss
 ible applications to the regularity theory of quasi-linear elliptic PDEs. 
 \nThe results to be presented are based on a recent preprint [1] in joint 
 work with Marc Hovemann (Marburg).\n\n[1] M.~Hovemann and M.~Weimar. Oscil
 lations and differences in Triebel-Lizorkin-Morrey spaces. Submitted prepr
 int (arXiv:2306.15239)\, 2023.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor I. Skrypnik (Institute Applied Mathematics and Mechanics of t
 he NAS Ukraine)
DTSTART:20231205T130000Z
DTEND:20231205T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/89
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/89/">Some remarks on the weak Harnack  inequality for unbounded 
 minimizers of elliptic functionals with  generalized Orlicz growth</a>\nby
  Igor I. Skrypnik (Institute Applied Mathematics and Mechanics of the NAS 
 Ukraine) as part of Function spaces\n\n\nAbstract\nWe prove the weak Harna
 ck type inequalities for nonnegative unbounded minimizers of  correspondin
 g elliptic functionals under the non-logarithmic \nZhikov's conditions\, r
 oughly speaking we consider the following De Giorgi's classes\n$$\n\\int\\
 limits_{B_{(1-\\sigma)r}(x_{0})}\\varPhi\\Big(x\,|(u-k)_{-}|\\Big)\\\,dx \
 \leqslant \\gamma \\int\\limits_{B_{r}(x_{0})}\\varPhi\\Big(x\,\\frac{(u-k
 )_{-}}{\\sigma r}\\Big)\\\,dx\,\n$$\n$\\sigma$\, $r\\in(0\,1)$\, $k>0$ and
  $\\varPhi(x\,\\cdot)$ satisfies the so-called ($p\,q$)-growth conditions.
  We are interesting in the case when \n$\\gamma$ depends on $r$\, it turns
  out that in this case it is impossible to use standard classical techniqu
 es. Our results cover new cases of  double-phase\, degenerate double-phase
  functionals\, non uniformly elliptic functionals  and functionals with va
 riable exponents.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emiel Lorist (Delft University of Technology)
DTSTART:20231219T130000Z
DTEND:20231219T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/90
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/90/">A discrete framework for the interpolation of Banach spaces
 </a>\nby Emiel Lorist (Delft University of Technology) as part of Function
  spaces\n\n\nAbstract\nInterpolation of bounded linear operators on Banach
  spaces is a widely used technique in analysis. Key roles are played by th
 e real and complex interpolation methods\, but there is also a wealth of o
 ther interpolation methods\, for example relevant in the study of (S)PDE. 
 In this talk I will introduce interpolation of Banach spaces using a new\,
  discrete framework. I will discuss how this framework extends and unifies
  various results in the literature. Moreover\, I will discuss its applicat
 ions to parabolic boundary value problems.\nThis talk is based on joint wo
 rk with Nick Lindemulder (Radboud University Nijmegen).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Duncan (ICMAT Madrid)
DTSTART:20231121T130000Z
DTEND:20231121T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/91
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/91/">Brascamp-Lieb Inequalities: Their Theory and Some Applicati
 ons</a>\nby Jennifer Duncan (ICMAT Madrid) as part of Function spaces\n\n\
 nAbstract\nThe Brascamp-Lieb inequalities form a class of multilinear ineq
 ualities that includes a variety of well-known classical results\, such as
  Hölder’s inequality\, Young’s convolution inequality\, and the Loomi
 s-Whitney inequality\, for example. Their theory is surprisingly multiface
 ted\, involving ideas from semigroup interpolation\, convex optimisation\,
  and abstract algebra. In the first half of this talk\, we will discuss so
 me of the key aspects of this theory and some important variants on the Br
 ascamp-Lieb framework\; in the second half\, we will talk specifically abo
 ut how these inequalities arise in harmonic analysis\, in particular about
  their use in fourier restriction theory and in recent results on the boun
 dedness of the helical maximal function. If time permits\, we will then ta
 lk about some more far-reaching connections with other areas of mathematic
 s and the sciences.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarnendu Sil (Indian Institute of Science Bengaluru)
DTSTART:20231107T130000Z
DTEND:20231107T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/92
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/92/">BMO estimates for Hodge-Maxwell systems with discontinuous 
 anisotropic coefficients</a>\nby Swarnendu Sil (Indian Institute of Scienc
 e Bengaluru) as part of Function spaces\n\n\nAbstract\nThe time-harmonic M
 axwell system in a bounded domain is \n		$$\n	\\left\\lbrace \\begin{align
 ed}\n			curl  H  &=  i\\omega \\varepsilon \\left(x\\right) E + J_{e}    \
 n				&&\\text{ in } \\Omega\, \\\\\n				\\operatorname*{curl} E &= -i\\ome
 ga \\mu\\left(x\\right) H + J_{m}     &&\\text{ in } \\Omega\, \\\\\n				\
 \nu \\times E &= \\nu \\times E_{0} &&\\text{  on } \\partial\\Omega\,\n		
 	\\end{aligned} \n			\\right.\n		$$\n		where $E\, H$ are unknown vector fi
 elds\, $E_{0}\, J_{e}\, J_{m}$ are given vector fields and $\\varepsilon\,
  \\mu$ are given $3\\times 3$ matrix fields which are bounded\, measurable
  and uniformly elliptic. When $\\varepsilon\, \\mu$ have sufficient regula
 rity\, e.g. Lipschitz\, then one can show that $(E\, H)$ inherits the same
  regularity as $(J_{e}\, J_{m})$\, as long as $E_{0}$ is as regular. \n		\
 n		\\par In this talk\, we shall discuss the sharpest regularity assumptio
 ns on $\\varepsilon\, \\mu$ under which $(E\, H)$ inherits BMO regularity 
 from $(J_{e}\, J_{m}).$  As it turns out\, the minimal regularity assumpti
 on on $\\varepsilon\, \\mu$ is that their components belong to a class of 
 `small multipliers of BMO'. This class neither contains nor is contained i
 n $C^{0}.$ Thus our results prove the validity of BMO estimates for a clas
 s of discontinuous coefficients. Our results are actually holds more gener
 ally\, for systems of differential $k$-forms of similar type in any dimens
 ion $n \\geq 3.$ \n		\n		\\par This is a joint work with my post-doctoral 
 student Dharmendra Kumar.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kim  Myyryläinen (Aalto University)
DTSTART:20240220T130000Z
DTEND:20240220T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/93
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/93/">Parabolic Muckenhoupt weights</a>\nby Kim  Myyryläinen (Aa
 lto University) as part of Function spaces\n\n\nAbstract\nWe discuss parab
 olic Muckenhoupt weights related to a doubly nonlinear parabolic partial d
 ifferential equation (PDE). In the natural geometry of the PDE\, the time 
 variable scales to the power in the structural conditions for the PDE. Con
 sequently\, the Euclidean balls and cubes are replaced by parabolic rectan
 gles respecting this scaling in all estimates. The main challenge is that 
 in the definition of parabolic Muckenhoupt weights one of the integral ave
 rages is evaluated in the past and the other one in the future with a time
  lag between the averages. Another main motivation is that the parabolic t
 heory is a higher dimensional version of the one-sided setting and the cor
 responding one-sided maximal function.\nThe main results include a charact
 erization of weak and strong type weighted norm inequalities for forward i
 n time parabolic maximal functions and parabolic versions of the Jones fac
 torization and the Coifman--Rochberg characterization. In addition to para
 bolic Muckenhoupt weights\, the class of parabolic $A_\\infty$ weights is 
 discussed from the perspective of parabolic reverse H\\"older inequalities
 . We consider several characterizations and self-improving properties for 
 this class of weights and study their connection to parabolic Muckenhoupt 
 conditions. A sufficient condition is given for the implication from parab
 olic reverse Holder classes to parabolic Muckenhoupt classes.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Brasco (Università degli Studi di Ferrara)
DTSTART:20240319T130000Z
DTEND:20240319T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/94
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/94/">Around Hardy's inequality for convex sets</a>\nby Lorenzo B
 rasco (Università degli Studi di Ferrara) as part of Function spaces\n\n\
 nAbstract\nWe start by reviewing the classical Hardy inequality for convex
  sets.\nWe then discuss the counterpart of Hardy's inequality for the case
  of fractional Sobolev-Slobodecki\\u{\\i} spaces\, still in the case of op
 en convex subsets of the Euclidean space. In particular\, we determine the
  sharp constant in this inequality\, by constructing explicit supersolutio
 ns based on the distance function.\nWe also show that this method works on
 ly for the {\\it mildly nonlocal} regime and it is bound to fail for the {
 \\it strongly nonlocal} one. We conclude by presenting some open problems.
 \n\\par\nSome of the results presented are issued from papers in collabora
 tion with Francesca Bianchi (Ferrara \\& Parma)\, Eleonora Cinti (Bologna)
 \, Firoj Sk (Oldenburg) and Anna Chiara Zagati (Ferrara \\& Parma).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Firoj Sk (University of Oldenburg)
DTSTART:20240402T120000Z
DTEND:20240402T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/95
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/95/">On Morrey's inequality in fractional Sobolev spaces.</a>\nb
 y Firoj Sk (University of Oldenburg) as part of Function spaces\n\n\nAbstr
 act\nWe study the sharp constant in Morrey's inequality for fractional Sob
 olev spaces on the entire Euclidean space of dimension N\, when 0<s<1 and 
 p>1 are such that sp>N. In a series of recent articles by Hynd and Seuffer
 t\, we discuss the existence of the Morrrey extremals together with some r
 egularity results. We analyse the sharp asymptotic behaviour of the Morrey
  constant in the following cases:\n\ni) when N\, p are fixed with N<p\, an
 d s go to N/p\,\n\nii) when s\, N are fixed\, and p tends to infinity\,\n\
 niii) when N\, p are fixed with N<p\, and s goes to 1. \n\nWe further demo
 nstrate the convergence of extremals as s goes to 1\, which ensures the co
 nsistency of the well-known local results by Hynd and Seuffert. This talk 
 is based on joint works with L. Brasco and F. Prinari.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rémy Rodiac (University of Warsaw)
DTSTART:20240305T130000Z
DTEND:20240305T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/96
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/96/">A relaxation approach for the minimisation of the neo-Hooke
 an energy</a>\nby Rémy Rodiac (University of Warsaw) as part of Function 
 spaces\n\n\nAbstract\nThe neo-Hookean model is a famous model for elastic 
 materials. However it is still not known if the neo-Hookean energy admits 
 a minimiser in an appropriate function space in 3D. I will explain what is
  the difficulty one encounters when we try to apply the direct method of c
 alculus of variations to this problem: this is the lack of compactness of 
 the minimisation space. I will also present a relaxation approach whose ai
 m is to transform the problem of lack of compactness into a problem of reg
 ularity for a modified problem. The talk will be based on joint works with
  M. Barchiesi\, C. Mora-Corral and D. Henao.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil Airta (University of Málaga)
DTSTART:20240416T120000Z
DTEND:20240416T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/97
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/97/">Singular integrals: Multiparameter framework and Zygmund di
 lation</a>\nby Emil Airta (University of Málaga) as part of Function spac
 es\n\n\nAbstract\nOver a half-century ago\, Alberto Calderón and Antoni Z
 ygmund made groundbreaking studies that initiated the study of modern harm
 onic analysis that focuses on singular integrals.\nThese operators still l
 ie at the core of today's harmonic analysis.\nRecently\, studies of singul
 ar integrals have been fast-paced due to new techniques that are based on 
 similar underlying methods as in the classical studies by Calderón and Zy
 gmund.\nThese new techniques\, namely the sparse method and the representa
 tion theory\, have enabled us to find\, for example\, sharp weighted estim
 ates and handle more complex operators such as multiparameter singular int
 egrals.\nMultiparameter framework refers to the study of singular integral
 s whose singularity is more delicate to work with as it is expanded over t
 he underlying space.\nIn this talk\, I will be giving an introduction to t
 he study of singular integrals and extensions to the multiparameter framew
 ork\, where we will be focusing\, especially on the kernels that are dilat
 ion invariant under a specific "entangled" dilation - the so-called Zygmun
 d dilation.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentina Ciccone (University of Bonn)
DTSTART:20240430T120000Z
DTEND:20240430T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/98
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/98/">Endpoint estimates for higher-order Marcinkiewicz multiplie
 rs</a>\nby Valentina Ciccone (University of Bonn) as part of Function spac
 es\n\n\nAbstract\nMarcinkiewicz multipliers on the real line are bounded f
 unctions of uniformly bounded variation \non each Littlewood-Paley dyadic 
 interval.  \nThe corresponding multiplier operators are well known to be b
 ounded on $L^p(\\mathbb{R})$ for all $1< p< \\infty$. Optimal weak-type en
 dpoint estimates for these operators have been studied by Tao and Wright w
 ho proved that \nthey map locally $L\\log^{1/2}L$ to weak $L^1$.\n\nIn thi
 s talk\, we consider higher-order Marcinkiewicz multipliers\, that is mult
 ipliers of uniformly bounded variation on each interval arising from a hig
 her-order lacunary partition of the real line. We discuss optimal weak-typ
 e endpoint estimates for the corresponding multiplier operators. \nThese a
 re established as a consequence of a more general endpoint result \nfor a 
 higher-order variant of a class of multipliers introduced by Coifman\, Rub
 io de Francia\, and Semmes and further studied by Tao and Wright.\n\n\nThe
  seminar is based on joint work with Odysseas Bakas\, Ioannis Parissis\, a
 nd Marco Vitturi.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arran Fernandez (Eastern Mediterranean University)
DTSTART:20240423T120000Z
DTEND:20240423T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/99
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/99/">Function spaces for fractional integrals and derivatives</a
 >\nby Arran Fernandez (Eastern Mediterranean University) as part of Functi
 on spaces\n\n\nAbstract\nFractional calculus investigates the generalisati
 on of derivatives and integrals to orders outside of the integers. Unlike 
 classical derivatives and integrals\, fractional-order operators do not ha
 ve a single unique definition\, but many competing formulae which can be c
 ategorised into broader families of operators. An immediate concern arisin
 g\, when such operators are defined\, is the question of what spaces they 
 act on and between. This talk will attempt to provide an overview of some 
 of the commonly used function spaces for fractional integrals and derivati
 ves\, with some discussion of their advantages and disadvantages according
  to the purposes at hand. If time allows\, some discussion of generalised 
 fractional-calculus operators will also be included\, with notes on whethe
 r the same function spaces can be used or must be modified when we extend 
 from classical to generalised settings.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Evseev (Okinawa Institute of Science and Technology)
DTSTART:20241001T120000Z
DTEND:20241001T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/100
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/100/">Weakly weakly* differentiable functions</a>\nby Nikita Evs
 eev (Okinawa Institute of Science and Technology) as part of Function spac
 es\n\n\nAbstract\nWe discuss various notions of weak differentiability of 
 Banach-valued functions. There is the theory of Sobolev spaces of Banach-v
 alued functions built on the notion of weak derivatives. In most issues\, 
 it reproduces properties from the real-valued case. However\, this approac
 h is not consistent with its metric counterpart. To overcome this\, one wo
 uld employ weak weak* derivatives. The properties of the last ones are far
  beyond the scalar case (for instance\, those derivatives need not be uniq
 ue or measurable). On the other hand\, it allows us to define Sobolev mapp
 ings valued in a metric space via isometric embedding of the metric space 
 into a Banach space.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linus Behn (Bielefeld University)
DTSTART:20241015T120000Z
DTEND:20241015T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/101
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/101/">Nonlocal equations with degenerate weights</a>\nby Linus B
 ehn (Bielefeld University) as part of Function spaces\n\n\nAbstract\nWe gi
 ve a definition for fractional weighted Sobolev spaces with degenerate\nwe
 ights. We provide embeddings and Poincare inequalities for these spaces an
 d\nshow robust convergence when the parameter of fractional differentiabil
 ity goes\nto 1. Moreover\, we prove local H¨older continuity and Harnack 
 inequalities for\nsolutions to the corresponding weighted nonlocal integro
 differential equations.\nJoint work with Lars Diening (Bielefeld)\, Jihoon
  Ok (Seoul)\, and Julian Rolfes\n(Bielefeld).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Detaille (Université Claude Bernard Lyon 1)
DTSTART:20241112T130000Z
DTEND:20241112T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/102
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/102/">Sobolev mappings to manifolds: when geometric analysis int
 eracts with function spaces</a>\nby Antoine Detaille (Université Claude B
 ernard Lyon 1) as part of Function spaces\n\n\nAbstract\nIn many applicati
 ons to problems coming e.g. from physics or\nnumerical methods\, it is nat
 ural to consider Sobolev mappings that are\nconstrained to take their valu
 es into a given manifold.\nAlthough being defined as a subset of a classic
 al Sobolev space of\nvector-valued maps\, the Sobolev space of mappings ta
 king their values\ninto a given manifold may have striking qualitatively d
 ifferent properties.\nIn this talk\, we will explain some selected problem
 s arising in the\nstudy of these manifold-valued Sobolev mappings.\nThe go
 al will be twofold: (1) give an insight on why these problems are\ninteres
 ting and what are the key phenomena at work there\, and (2)\nillustrate ho
 w geometric analysis can give incentive to study classical\n(real-valued) 
 function spaces\, and combine the tools produced in this\nprocess with geo
 metric tools in order to solve challenging problems.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela Di Donato (University of Pavia)
DTSTART:20241029T130000Z
DTEND:20241029T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/103
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/103/">Rectifiability in Carnot groups</a>\nby Daniela Di Donato 
 (University of Pavia) as part of Function spaces\n\n\nAbstract\nIntrinsic 
 regular surfaces in Carnot groups play the same role as C^1 surfaces in Eu
 clidean spaces. As in Euclidean spaces\, intrinsic regular surfaces can be
  locally defined in different ways: e.g. as non critical level sets or as 
 continuously intrinsic differentiable graphs. The equivalence of these nat
 ural definitions is the problem that we are studying. Precisely our aim is
  to generalize some results proved by Ambrosio\, Serra Cassano\, Vittone v
 alid in Heisenberg groups to the more general setting of Carnot groups. Th
 is is joint work with Antonelli\, Don and Le Donne\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Lerner (Bar-Ilan University)
DTSTART:20241203T130000Z
DTEND:20241203T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/104
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/104/">On some quantitative weighted weak type inequalities</a>\n
 by Andrei Lerner (Bar-Ilan University) as part of Function spaces\n\n\nAbs
 tract\nIn this talk I will discuss quantitative weighted weak type inequal
 ities of Muckenhoupt--Wheeden type\, both in the matrix and scalar setting
 s.In particular\, in the matrix setting we obtain the sharp bound for the 
 Christ--Goldberg maximal operator in the range $p \\in (1\,2)$.Also\, in t
 he scalar setting\,\nwe obtain an improved bound for Calderon--Zygmund ope
 rators in the range $p\\in (1\,p^*)$\, where $p^*$ is the root of the cubi
 c equation $p^3-2p^2+p-1=0$.\n\nThe talk is based on joint work with Kangw
 ei Li\, Sheldy Ombrosi and Israel Rivera-Ríos.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duvan Henao (Instituto de Ciencias de la Ingeniería\, Universidad
  de O’Higgins)
DTSTART:20250408T120000Z
DTEND:20250408T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/105
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/105/">NeoHookean energies\, cavitation\, and relaxation in nonli
 near elasticity</a>\nby Duvan Henao (Instituto de Ciencias de la Ingenier
 ía\, Universidad de O’Higgins) as part of Function spaces\n\n\nAbstract
 \nThe neoHookean model is one of the most commonly used approaches to stud
 y the mechanical response of elastic bodies undergoing large deformations.
  However\, the neoHookean energy is expected to possess no minimizers in t
 he Sobolev class naturally associated to its quadratic coercivity. This is
  connected to the formation and sudden expansion of voids observed in conf
 ined elastomers. There is analytical evidence for the conjecture that the 
 nonexistence is due to the opening of an ever larger number of cavities. R
 egularizations of the neoHookean model either impose a length-scale for th
 e cavities created (with a second gradient\, or taking into account the en
 ergy required to stretch the created surface) or impose a bound in the num
 ber of cavities that the body is allowed to open. In the second approach\,
  the first existence results are due to Henao & Rodiac (2018) in the axisy
 mmetric class for hollow domains\, and to Doležalová\, Hencl & Molchanov
 a (2024) in the weak closure of homeomorphisms in 3D. In more general clas
 ses where harmonic dipoles are admitted\, a relaxation approach has been p
 roposed by Barchiesi\, Henao\, Mora-Corral & Rodiac (2023\, 2024)\, where 
 the mass of the singular part of the derivative of the inverse is found to
  accurately give the cost of creating dipole singularities.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Mora-Corral (Universidad Autónoma de Madrid)
DTSTART:20250225T130000Z
DTEND:20250225T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/106
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/106/">Invertibility conditions for Sobolev maps</a>\nby Carlos M
 ora-Corral (Universidad Autónoma de Madrid) as part of Function spaces\n\
 n\nAbstract\nIn nonlinear elasticity\, a deformation is represented by a S
 obolev map. In order to be physically acceptable\, the deformation must pr
 eserve the orientation and cannot interpenetrate matter. There are several
  ways to model mathematically these restrictions\, but a popular choice is
  that the deformation must have positive Jacobian and be injective (almost
  everywhere). The first restriction is local and the second is global. In 
 this talk I will review some theorems guaranteeing injectivity from the po
 sitivity of the Jacobian together with other assumptions. As a consequence
 \, I will present results on the existence of injective minimizers for ela
 stic energies.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Dragičević (University of Ljubljana)
DTSTART:20250422T120000Z
DTEND:20250422T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/107
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/107/">The $p$-ellipticity condition for systems of partial diffe
 rential equations with complex coefficients</a>\nby Oliver Dragičević (U
 niversity of Ljubljana) as part of Function spaces\n\n\nAbstract\nWe exten
 d the concept of $p$-ellipticity for (single) elliptic operators\, that we
  introduced in 2016\, to the case of systems of elliptic equations with co
 mplex coefficients. We prove several key properties of $p$-ellipticity aki
 n to those that have been known to hold in the scalar case. In some respec
 ts\, however\, the vector case fundamentally differs from the scalar one.\
 n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandros Eskenazis (Sorbonne Université and University of Cambr
 idge)
DTSTART:20250325T130000Z
DTEND:20250325T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/109
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/109/">Discrete logarithmic Sobolev inequalities in Banach spaces
 </a>\nby Alexandros Eskenazis (Sorbonne Université and University of Camb
 ridge) as part of Function spaces\n\n\nAbstract\nWe shall discuss certain 
 aspects of vector-valued harmonic analysis on the discrete hypercube. Afte
 r presenting classical scalar-valued inequalities going back to Talagrand
 ’s work in the 1990s\, we will survey recent developments on vector-valu
 ed Poincaré inequalities. Then\, we will proceed to present a new optimal
  vector-valued logarithmic Sobolev inequality in this context. The talk is
  based on joint work with D. Cordero-Erausquin (Sorbonne).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dariusz Kosz (Wroclaw University of Science and Technology)
DTSTART:20250311T130000Z
DTEND:20250311T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/110
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/110/">Variation of the centered maximal function</a>\nby Dariusz
  Kosz (Wroclaw University of Science and Technology) as part of Function s
 paces\n\n\nAbstract\nLet M be the centered Hardy–Littlewood maximal oper
 ator on the real line. Is it true that the total variation of the maximal 
 function Mf does not exceed the total variation of f?\n\nIn this talk\, I 
 verify this conjecture for simple functions with zero and nonzero values a
 lternating. I also discuss a strengthened version of the conjecture and th
 e equivalence of the continuous and discrete settings in this context.\n\n
 My talk is based on a joint project with Paul Hagelstein and Krzysztof Ste
 mpak.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Oikari (University of Helsinki)
DTSTART:20250429T120000Z
DTEND:20250429T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/111
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/111/">Global exponential integrability of parabolic BMO function
 s</a>\nby Tuomas Oikari (University of Helsinki) as part of Function space
 s\n\n\nAbstract\nA result of Smith and Stegenga from the '90s states that 
 in domains $\\Omega\\subset\\mathbb{R}^n$ functions of bounded mean oscill
 ation $\\mathrm{BMO}(\\Omega) \\subset \\mathrm{EI}(\\Omega)$ are globally
  exponentially integrable if and only if $\\Omega$ satisfies a quasihyperb
 olic boundary condition. This is a geometric characterization of an embedd
 ing between function spaces\, motivated by the global integrability of sol
 utions of elliptic PDEs on domains\, such as the Laplacian.\nFor parabolic
  PDEs on $\\mathbb{R}^{n}_x\\times\\mathbb{R}_t\,$ such as the parabolic $
 p$-Laplace\, the relevant space of interest is the forward-in-time parabol
 ic BMO\, a classical work of Moser from the '60s.\nIn this talk I discuss 
 a parallel of the result of Smith and Stegenga in the parabolic context of
  Moser\, where the embedding of interest and the quasihyperbolic boundary 
 condition both become oriented in time.\n\nThis talk is based on a joint w
 ork with Kim Myyryläinen and Olli Saari.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anders Björn (Linköping University)
DTSTART:20251125T130000Z
DTEND:20251125T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/112
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/112/">Quasicontinuouity of Newtonian Sobolev functions and outer
  capacities based on Banach function spaces</a>\nby Anders Björn (Linköp
 ing University) as part of Function spaces\n\n\nAbstract\nThe equivalence 
 classes in the (first-order real-valued) Sobolev space\n$W^{1\,p}$ are up 
 to a.e.\, but there are better\nrepresentatives.\n\nThe corresponding Newt
 onian Sobolev space $N^{1\,p}(\\mathcal{P})$\non a metric space $\\mathcal
 {P}$ is defined\nas those $L^p$ functions that have upper gradients in $L^
 p$.\nThis \nmakes them automatically better defined than a.e.\, since\nthe
  bad representatives lack upper gradients in $L^p$.\n\nIt has been an open
  problem since the late 1990s whether \nfunctions in $N^{1\,p}(\\mathcal{P
 })$ are\nalways quasicontinuous. \nThe most general results is due to \nEr
 iksson-Bique and Poggi-Corradini (2024) who showed this\nwhen $\\mathcal{P
 }$ is locally complete.\n\nQuasicontinuity is also closely connected to wh
 ether the\nassociated (Sobolev) capacity is an outer capacity.\n\nIn this 
 talk I will take a look at these questions \nif we replace the $L^p$ norm 
 by a more \ngeneral Banach function space/lattice norm.\nA particular focu
 s will be on $L^\\infty$.\n\nThis is based on joint work with Jana Björn 
 and Lukáš Malý.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Odysseas Bakas (University of Patras)
DTSTART:20251007T120000Z
DTEND:20251007T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/113
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/113/">A dyadic approach to the study of products of functions in
  $H^1$ and $BMO$</a>\nby Odysseas Bakas (University of Patras) as part of 
 Function spaces\n\n\nAbstract\nIt was shown by A. Bonami\, T. Iwaniec\, P.
  Jones\, and M. Zinsmeister that the product of a function in the Hardy sp
 ace $H^1(\\mathbb{D})$ and a function in $BMOA(\\mathbb{D})$ belongs to th
 e Hardy-Orlicz space $H^{\\log}(\\mathbb{D})$\, and that every function in
  $H^{\\log}(\\mathbb{D})$ can be written as such a product.\n\nIn this tal
 k\, we present a dyadic approach to the study of products of functions in 
 $H^1$ and $BMO$\, as well as to the study of the associated Hardy-Orlicz s
 paces.\n\nThe talk is based on joint work with Sandra Pott\, Salvador Rodr
 íguez-López\, and Alan Sola.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Alexis (University of Bonn)
DTSTART:20251111T130000Z
DTEND:20251111T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/114
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/114/">How to represent a function in a quantum computer</a>\nby 
 Michel Alexis (University of Bonn) as part of Function spaces\n\n\nAbstrac
 t\nWe define the SU(2)-valued nonlinear Fourier transform and explain its 
 connection with quantum signal processing. In particular\, we provide an a
 lgorithm to compute the inverse nonlinear Fourier transform in a special c
 ase\, which allows one to represent most functions in a quantum computer. 
 Finally\, we mention the higher dimensional analog with the SU(2n)-valued 
 nonlinear Fourier transform. This talk includes joint work with L. Becker\
 , L. Lin\, G. Mnatsakanyan\, D. Oliveira e Silva\, C. Thiele and J. Wang.\
 n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Alberto Antonini (National Institute of High Mathematics (In
 DAM)\, University of Florence\, Italy)
DTSTART:20251021T120000Z
DTEND:20251021T130000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/115
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/115/">Second-order estimates in anisotropic elliptic problems</a
 >\nby Carlo Alberto Antonini (National Institute of High Mathematics (InDA
 M)\, University of Florence\, Italy) as part of Function spaces\n\n\nAbstr
 act\nIn recent years\, various results showed that second-order regularity
  of  solutions to the $p$-Laplace equation \n$$\n     -\\Delta_p u=-\\math
 rm{div}\\big(|\\nabla u|^{p-2}\\nabla u \\big)=f\,\\quad p>1\,\n$$\ncan be
  properly formulated in terms of the expression under the divergence\, the
  so-called stress field\, see [3].\n\n \n I will discuss the extension of 
 these results to the anisotropic $p$-Laplace problem\, namely equations of
  the kind\n$$\n-\\mathrm{div}\\\,\\big(\\mathcal{A}(\\nabla u)\\big)=f\\\,
 \,\n$$\n in which the stress field is given by $\\mathcal{A}(\\nabla u)=H^
 {p-1}(\\nabla u)\\\,\\nabla_\\xi H(\\nabla u)$\, where $H(\\xi)$ is a norm
  on $\\mathbb{R}^n$ satisfying suitable ellipticity assumptions.\n\n$W^{1\
 ,2}$-Sobolev regularity of $\\mathcal{A}(\\nabla u)$ is established when $
 f$ is square integrable\, and both local and global estimates are obtained
 . The latter apply to solutions to homogeneous Dirichlet problems on suffi
 ciently regular domains.\nA key point in our proof is an extension of Reil
 ly's identity to the anisotropic setting.\n\nThis is based on joint works 
 with A. Cianchi\, G. Ciraolo\, A.\nFarina and V.G. Maz'ya.\n\n  \n[1]  C.A
 . Antonini\, G. Ciraolo\, A. Farina\, Interior regularity results for inho
 mogeneous anisotropic quasilinear equations\, Math. Ann. (2023).\n \n\n[2]
  C.A. Antonini\, A. Cianchi\, G. Ciraolo\, A. Farina\, V.G. Maz'ya\, Globa
 l second-order estimates in anisotropic elliptic problems\, Proc. Lond. Ma
 th. Soc. (3)\, vol. 130\, no. 3\, 60 pp.\, (2025)\n\n[3] A. Cianchi\, V.G.
  Maz'ya\, Second-order two-sided estimates in nonlinear elliptic problems\
 , Arch. Ration. Mech. Anal. 229 (2018)\, no. 2\, 569-599.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Georg Feichtinger (University of Vienna)
DTSTART:20251216T130000Z
DTEND:20251216T140000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/116
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/116/">What is a Continuous Orthonormal Basis? How the Ideas used
  in Physics can be put on a Sound Mathematical Ground</a>\nby Hans Georg F
 eichtinger (University of Vienna) as part of Function spaces\n\n\nAbstract
 \nWhen it comes to the use of the family of Dirac measures on the real lin
 e of the Euclidean space R^d physicist and engineers often use weird formu
 las\, involving divergent integrals\, which are often manipulated in a for
 mal way\, based on the analogy to the finite discrete case\, where such ma
 nipulations are justified within linear algebra.\n\nThe talk is going to d
 escribe some ongoing discussion which aims at a mathematically sound descr
 iption of such formal manipulations in the context of mild distributions. 
 Mild distributions form together with the Hilbert space L2(R^d) and the un
 derlying Banach algebra S_0(R^d) of test functions (the Feichtinger algebr
 a) a so-called Banach Gelfand triple or rigged Hilbert space\, comparable 
 with the Schwartz setting leading to (the much larger space of) tempered d
 istributions.\n\nUsing this setting the claim that the (continuous) Fourie
 r transform is nothing else but a change of basis\, moving from the Dirac 
 basis to the (equivalent) Fourier basis\, makes sense and can be very well
  justified.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iker Gardeazabal Gutiérrez
DTSTART:20260225T094000Z
DTEND:20260225T104000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/117
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/117/">Self-improving properties of generalized Poincaré inequal
 ities</a>\nby Iker Gardeazabal Gutiérrez as part of Function spaces\n\n\n
 Abstract\nIn this talk\, we will discuss a method to obtain extensions of 
 the classical Poincaré-Sobolev inequalities. The main tools of this metho
 d are the different forms of self-improving properties that the generalize
 d Poincaré inequalities satisfy. The first part of the talk will focus on
  these self-improving properties\, including some recent improvements\, wh
 ile the second part will present some applications of this method.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spyridon Kakaroumpas (University of Würzburg)
DTSTART:20260325T094000Z
DTEND:20260325T104000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/118
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/118/">Multilinear singular integral theory for matrix weights</a
 >\nby Spyridon Kakaroumpas (University of Würzburg) as part of Function s
 paces\n\n\nAbstract\nThe action of classical operators such as maximal fun
 ctions or the Hilbert transform on weighted Lebesgue spaces is one of the 
 main topics of interest in harmonic analysis. In this talk we discuss a re
 cent development of a novel\, multilinear singular integral theory that in
 corporates matrix weights. First\, we develop from scratch a theory of mul
 tilinear Muckenhoupt classes for matrix weights\, using techniques inspire
 d from convex combinatorics and differential geometry. Next\, we fully cha
 racterize the action of multilinear Calderón--Zygmund operators and (sub)
 multilinear maximal functions on cartesian products of matrix weighted Leb
 esgue spaces. On the one hand\, we develop new versions of standard locali
 zation techniques such as sparse domination and Reverse Hölder inequaliti
 es. On the other hand\, we introduce a new concept of directional non-dege
 neracy for integral kernels. Thus\, we generalize and unify several previo
 us results of the scalar and/or linear theories.\n\nThis talk is based on 
 joint work with Dr. Zoe Nieraeth (Instituto de Matemáticas Universidad de
  Sevilla (IMUS)).\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Predojević (University of Zagreb)
DTSTART:20260311T094000Z
DTEND:20260311T104000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/119
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/119/">Joint upper Banach density\, VC dimension\, and Euclidean 
 point configurations</a>\nby Bruno Predojević (University of Zagreb) as p
 art of Function spaces\n\n\nAbstract\nWe present two related results conce
 rning the existence of large copies\nof Euclidean point configurations in 
 large sets.\nThe first result generalises a classic conjecture of Szekély
 . More precisely\,\nwe provide a sufficient condition on two measurable su
 bsets of the plane that\nensures all sufficiently large distances between 
 them are realised.\nThe second result concerns the Vapnik–Chervonenkis d
 imension of a certain\ngeometric family of sets. Specifically\, for a suff
 iciently regular curve $\\Gamma$ and for all\nsufficiently large scales $t
 >0$\, we show that the family consisting of portions of\ntranslates of $t\
 \Gamma$ attains the maximal possible Vapnik–Chervonenkis dimension.\nThe
 se two seemingly distinct problems are unified by a new notion that we\nin
 troduce in the talk: Joint upper Banach density.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Israel Pablo Rivera Ríos (University of Málaga)
DTSTART:20260506T084000Z
DTEND:20260506T094000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/120
DESCRIPTION:by Israel Pablo Rivera Ríos (University of Málaga) as part o
 f Function spaces\n\nInteractive livestream: https://cesnet.zoom.us/j/9982
 5599862\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/120/
URL:https://cesnet.zoom.us/j/99825599862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen Qi Zhang (Australian National University)
DTSTART:20260408T084000Z
DTEND:20260408T094000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/121
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Funct
 ionSpaces/121/">Stein-Weiss and power weight Sobolev inequalities in $L^1$
 </a>\nby Wen Qi Zhang (Australian National University) as part of Function
  spaces\n\nInteractive livestream: https://cesnet.zoom.us/j/99825599862\n\
 nAbstract\nIt is known that $L^1$ Stein-Weiss (and Sobolev) inequalities f
 ollow a slightly different pattern than their $L^p$\, $p>1$ counterparts. 
 They serve as weaker replacement inequalities for the failure of $L^1$ ine
 qualities between differential operators. Recently\, P. De Napoli and T. P
 icon were able to make progress in this area by using the canceling/cocanc
 eling framework introduced by J. Van Schaftingen. Inspired by their work\,
  we investigate if these results can be relaxed (in a subcritical case) an
 d if their results can be extended to a critical case. We discuss and revi
 ew some of the constraints encountered in these areas.\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/121/
URL:https://cesnet.zoom.us/j/99825599862
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riju Basak (National Taiwan Normal University)
DTSTART:20260422T084000Z
DTEND:20260422T094000Z
DTSTAMP:20260404T093456Z
UID:FunctionSpaces/122
DESCRIPTION:by Riju Basak (National Taiwan Normal University) as part of F
 unction spaces\n\nInteractive livestream: https://cesnet.zoom.us/j/9982559
 9862\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FunctionSpaces/122/
URL:https://cesnet.zoom.us/j/99825599862
END:VEVENT
END:VCALENDAR