*The Prague seminar on function
spaces*

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

2018

Friedrichs inequality in weighted spaces - amalgams in $L\sp p$ and $L\sp q$ (joint work with H.P. Heinig)

Poincaré and Friedrichs inequality in Orlicz-Sobolev spaces (joint work with D.E. Edmunds and L. Pick)

Approximation property of weighted Orlicz spaces (joint work with L. Pick)

$A_\infty$ conditions on $\Bbb R\sp 1$ with general measure (joint work with L. Pick)

The Hardy operator, $L\sp\infty$, and BMO (joint work with Q. Lai)

Weighted inequalities for the Hardy operator in Orlicz classes

Density of smooth functions in the space $W\sp{k,p(x)}(\Omega)$ (joint work with D.E. Edmunds)

Weighted norm inequalities involving gradients (paper by C. Carton-Lebrun and H.P. Heinig)

Traces of a weighted Sobolev space

Inequalities by majorization (from a book by A. Marshall and J. Olkin)

One-sided better $\lambda$-inequalities

Traces of weighted Sobolev spaces (joint work with A. Nekvinda)

Weighted inequalities and degenerate elliptic PDEs (paper by E.W. Stredulinsky)

Some Young type inequalities with applications

Reverse Hölder inequalities withconstants close to 1 (paper by I. Wik)

Smooth approximations of Sobolev functions on planar domains (paper by W. Smith, A. Stanoyevitch and D.A. Stenenga)

Inequalities of Hardy type

Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator (paper by S. Bloom and R. Kerman)

Compactness of Hardy-type operators in weighted Banach function spaces (joint work with D.E. Edmunds and P. Gurka)

Poincaré inequalities and Minkowski dimension

Hardy inequalities on trees (joint work with D.J. Harris and L. Pick)

Poincaré inequalities on trees (joint work with W.D. Evans and D.J. Harris)

Approximation of functions by generalized sampling series

Double exponential integrability of convolution operators in generalized Lorentz-Zygmund spaces (joint work with D.E. Edmunds and P. Gurka)

Two-weight Hardy inequality

Weighted inequalities for resolvent of spectrum of Riemann-Liouville operator

Generalized ridged domains (paper by W.D. Evans and D.J. Harris)

Traces of weighted anisotropic Sobolev spaces (joint work with J. Lang)

Duality between gehring and Muckenhoupt classes (paper by M. Carozza)

The Hardy operator, $L\sp\infty$ and BMO

Banach Function Spaces (from a book by C. Bennett and R. Sharpley)

Muckenhoupt's and Sawyer's conditions for maximal operators (paper by Y. Rakotondratsimba)

Two limiting cases of Sobolev embeddings (joint work with D.E. Edmunds)

The Hardy constant (paper by E.B. Davies)

Hardy inequalities for fractional order derivatives

Two-weight inequality for fractional maximal operator (paper by R.L. Wheeden)

The Hardy operator and the gap between $L\sp\infty$ and BMO (joint work with J. Lang)

Difference between continuity and absolute continuity of norm in Banach function spaces (joint work with J. Lang)

Embeddings of weighted Orlicz-Lorentz spaces (joint work with M. Krbec)

Remarks on Poincaré inequalities (joint work with R.C. Brown and D.E. Edmunds)

Weighted Poincaré inequalities (joint work with D.E. Edmunds and A. Cianchi)

Self-adjoint boundary conditions of the Schrödinger operator

Interpolation inequality with Hölder norms

Elementary proof of Hardy's inequality (paper by G. Sinnamon and V. Stepanov)

Double exponential integrability, Bessel potentials and imbedding theorems (joint work with D.E. Edmunds and P. Gurka)

Imbeddings of weighted Orlicz-Lorentz spaces (joint work with J. Lang)

Continuity and absolute continuity of norm in Banach function spaces (joint work with J. Lang)

Sharpness of embeddings in logarithmic Sobolev spaces (joint work with D.E. Edmunds and B. Opic)

Interpolation of operators on scales of generalized Lorentz-Zygmund spaces (joint work with W.D. Evans and B. Opic)

Sharp Orlicz space inequalities for the Paley-Titchmarsh inequality)

Duality principle on the cone of monotone functions in Orlicz spaces

Hardy's inequality for derivatives of fractional order

Extrapolation theory and some of its applications to analysis

Sobolev embedding theorem for Orlicz spaces

Weighted strong type inequalities for integral transforms with positive kernels

Norm inequalities for derivatives and differences (book by M.K. Kwong and A. Zettl)

Atomic decomposition of Lizorkin-Triebel spaces with exponential weights

Indices in Orlicz spaces and applications to variational integrals (joint work with A. Fiorenza)

Limiting embeddings of weighted Sobolev spaces (joint work with T. Schott)

Extrapolation of reduced Sobolev embeddings (joint work with H.-J. Schmeisser)

N-dimensional weighted Hardy inequality

Maximal difference between continuity and absolute continuity of a norm in Banach function spaces (joint work with J. Lang)

Approximation numbers and entropy numbers of embeddings of fractional Besov-Sobolev spaces in Orlicz spaces (paper by H. Triebel)

The Hardy-Littlewood maximal function and Sobolev spaces on a metric space (paper by O. Martio)

On the adjoint of the maximal operator (paper by A. de la Torre)

Weighted mean convergence of Fourier-Jacobi series

Extrapolation from modular inequalities (joint work with S Bloom)

N-dimensional weighted inequalities

A note on Gehring's lemma (paper by M. Milman)

A note on reversed Hardy's inequalities (paper by M. Milman)

Weighted norm inequalities for general operators on monotone functions (paper by S. Lai)

Hardy's inequality of fractional order

H-transforms on spaces of p-summable functions

Boundedness of solutions of variational problems under general growth conditions

Regularity results about some Lagrange problems of calculus of variations

Grand $L\sp p$ spaces and applications

Optimal Sobolev embeddings on rearrangement-invariant spaces (joint works with D.E. Edmunds and R. Kerman, and with A. Cianchi)

Optimal Sobolev embeddings on rearrangement-invariant spaces (joint works with D.E. Edmunds and R. Kerman, and with A. Cianchi)

Existence and regularity of the Jacobian determinants in the framework of potential spaces

Some remarks to Hardy's inequality

Norms of embeddings of logarithmic Bessel potential spaces (joint work with D.E. Edmunds and B. Opic)

Boundedness of general kernel operators from a Banach Function space into $L\sp\infty$ (joint work with J. Lang and L. Pick)

Weighted mean convergence on semigroups (joint work with S. Thangavelu)

Weighted inequalities for monotone and convex functions (paper by H.P. Heinig and L. Maligranda)

Global limiting embeddings of logarithmic Bessel potential spaces (joint work with P. Gurka)

An optimal interpolation theorem of Marcinkiewicz type in Orlicz space

From Hardy's inequality to more general kernels

An inequality of Amemiya and Orlicz norms in Orlicz spaces

Bergman spaces in interpolation theory, two properties

Generalizations of Hardy inequalities (paper by H.P. Heinig and G. Sinnamon)

Boundedness of generalized Hardy operators (joint work with A. Gogatishvili)

Bending of a cusp plate with the profile of a general form

On the domain and range of the maximal operator (joint work with A. Fiorenza)

Pointwise and integral Hardy inequalities (paper by P. Hajlasz and J. Kinnunen, and joint work with D.E. Edmunds)

Geometry of inner maximal functions

On $L\sp{p(x)}$ norms

Some appendix to the Hardy inequality

Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces (paper by D.E. Edmunds and Yu. Netrusov)

Weighted inequalities for Hardy operator with monotone weights (the paper by J. Cerda and J. Martín)

Higher order Hardy inequalities

Interpolation inequalities for sums with three weights (joint work with R.C. Brown and D. Hinton)

Nonhomogeneous eigenvalue problems involving the p-Laplacian

Extrapolation characterization of exponential Orlicz spaces (joint work with D.E. Edmunds)

Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces (the paper by Yu. Netrusov and D.E. Edmunds)

Approximation numbers of Hardy operators (joint work with W.D. Evans and D.J. Harris)

Optimality of embeddings of logarithmic Bessel potential spaces (joint work with D.E. Edmunds and B. Opic)

On embeddings between classical Lorentz spaces (joint work with M. Carro, J. Soria and V.D. Stepanov)

Weighted inequalities for Volterra integral operators in Banach function spaces

Weighted inequalities for Volterra integral operators in Banach function spaces

Atomic decomposition in Bessel potential spaces

The maximal regularity problem (joint work with Gilles Lancier)

The dual of an optimal Sobolev domain (joint work with Ron Kerman)

Weighted norm inequalities for singular integrals and commutators (joint work with Carlos Pérez)

Sobolev classes on metric spaces

Sobolev embeddings with variable exponent

Limiting embeddings in function spaces of Besov type and entropy numbers

Reverse Hölder inequalities in Orlicz classes

Geometry of Hölder embeddings (joint work with Steve Buckley)

Unique continuation for a class of degenerate elliptic operators (joint work with T. Okaji)

Compactness of weighted embeddings

Decomposition in $L(\log L)\sp{\alpha}$

Elliptic equations with right hand side in Zygmund spaces

Boundary behaviour of absolutely continuous functions of several variables

Stokes and Navier-Stokes equations: An approach in Hardy and weighted Sobolev spaces

On equivalence between weak and strong inequalities for Sobolev functions

Nash implies Sobolev (joint work with Jan Malý)

Continuity of monotone functions

Sharp embeddings of Bessel potential spaces with logarithmic smoothness (joint work with Walter Trebels)

An elementary proof of sharp Sobolev embeddings (joint work with Jan Malý)

Duality principles and reduction theorems (joint work with Luboš Pick)

On the approximation numbers of Hardy-type operators on trees (joint work with Desmond J. Harris and Jan Lang)

Extrapolation theory on $L^p$ spaces

Yano's theorem and the dual result

Extrapolation theory for Lorentz spaces

Characterization of $\sum_r$ spaces of the family $L^{p,q}$

On the characterization of $\sum_p$ spaces

Second asymptotics of the approximation numbers of Volterra operators

Applications of a general theory of approximation spaces in classical analysis and approximation theory

A class of Young functions

Two - sided estimates for the approximation behavior of some linear means

Traces and Sobolev extension domains

Estimates of weak solutions of linear elliptic equations in weighted spaces (paper by A. Canale, L. Caso, M. Transirico: An extension of a theorem by C. Miranda in weighted spaces)

On maximal functions

On the uniqueness of maximal function

On reverse weak (1,1) type inequalities for maximal operators with respect to Borel measures

Some open problems from extrapolation theory

Sharp Sobolev embeddings and related Hardy inequalities (paper by David Edmunds and Hans Triebel)

Average operators on $\{l^{p_n}\}$ and $L^{p(x)}$

Sharp rearrangement estimates for Riesz potential in metric spaces (joint work with Jan Malý)

Rearrangement of Hardy-Littlewood maximal functions in Lorentz spaces (paper by J. Bastero, M. Milman and F. Ruiz)

New interpolation results for spaces of Lorentz-Zygmund type

Wolff potentials

Quasiregular mappings in non commutative geometry

Distribution and rearrangement estimates of the maximal function and interpolation (paper by I.U. Asekritova, N.Y. Krugljak, L. Maligranda and L.E. Persson).

On the extrapolation estimates (joint work with Amiran Gogatishvili).

Faktorization of positive definite matrix--functions and its applications to the Wiener--Kolmogorov prediction theory of stationary processes

Geometry of the Sobolev spaces on a regular metric tree and Hardy inequalities

Duality principle in Lorentz spaces and applications

Some recent results on interpolation of compact operators

Some questions about Sobolev spaces with variable exponent

On the zero modes of Pauli operators

New Extrapolation Estimates (paper by María Carro)

Rearrangement Inequality for the Ergodic Maximal Function

Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities (book by M.J. Carro, J.A. Raposo and J. Soria)

On Calderón's reproducing formula.

Dirichlet-Neuman bracketing in L^p,

On the zero modes of Pauli and Dirac operators,

Vector-valued function spaces and sharp embeddings.

Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities (book by M.J. Carro, J.A. Raposo and J. Soria)

Extrapolation theory for the real interpolation method (paper by María Carro)

The generalization of Stein-Weiss theorem for the ergodic Hilbert transform

Boundary value problems for analytic and harmonic functions with boundaries from Zygmund classes

Compact and non-compact maps

Equivalence of norms in $\ell^{p_n}$ spaces and the maximal operator on $L^{p(x)}(\mathbb{R}^n)$

A remark on classical Lorentz spaces

Functional with p(x)-growth and related issues

Maximal operator on $L^{p(x)}(R^n)$

A sharp form of an embedding into exponential and double exponential spaces

Logarithmic Sobolev Inequalities

Generalized Lebesgue and Sobolev Spaces

An analytic interpolation theorem with application to the boundedness of operators on weighted Lebesgue spaces.

Bessel-potential-type spaces and embeddings (limiting and super-limiting cases)

Boundedness and compactness of embeddings of logarithmic Bessel potential spaces

Problems of entropy numbers of compact embeddings of logarithmic Bessel potential spaces.

New function spaces and limiting Sobolev embeddings (paper by Bastero, Milman and Ruiz)

Optimal imbeddings of smoothness spaces

Some properties of function spaces with multiweighted derivatives

Elliptical problems in unbounded domains, with application to Navier-Stokes and Oseen equations

Weighted Hardy inequalities on classical Lorentz spaces (paper by Santiago Boza and Joaquim Martin)

Pointwise and topological behavior of mappings in certain Sobolev classes

L^p spaces with variable exponent

Various criteria for the validity of the Hardy inequality

A characterization of the spaces satisfying a result of Lions-Peetre type for N-tuples

An atomic approach to limiting embeddings for vector-valued function spaces

Hardy and Rellich inequalities associated with magnetic fields

Local growth envelopes for spaces of generalized smoothness: a unified treatment?

Subspaces and distances

Entropy function spaces and Interpolation

Special trigonometric functions, p-Laplacian and geometry of the Sobolev imbedding

The Gateway to Compactness

Relation between weights and equivalent expressions for norms in Lorentz spaces

Function spaces with dominating mixed smoothness - decompositions and entropy numbers

Sobolev capacity in variable exponent spaces

Functional properties of the space S_p(w)

Limiting reiteration for real interpolation with slowly-varying functions

Sharp Embeddings of Besov Spaces with Logarithmic Smoothness (An Elementary Approach)

Sharp embeddings of Besov spaces with Logarithmic Smoothess: The Limiting Case

Decomposition and extrapolation in spaces of integrable functions

New family of interpolation spaces and description of interpolation orbits

Topological and geometric structure of some Calderon-Lozanovskii spaces

Interpolation orbits and Orlicz spaces

Minimal and maximum extensions of interpolation functors and the generalized method of means

Medical imaging, Inverse Problems and Quasiconformal Maps

Optimality and Interpolation

Optimality and interpolation - remarks to certain results of R. Kerman and L. Pick

An equivalence theorem for some scales of integral conditions (joint work with A. Kufner, L.-E. Persson and A. Wedestig)

On non-effective weights in Orlicz spaces

A Strong-type Capacitary Inequality

Sharp generalized Trudinger inequalities via truncation

A Note on the Maximal Operator in $L\sp{p(x)}$

Basic topological and geometric structure of generalized Orlicz-Lorentz spaces. Part I - Global structure

Basic topological and geometric structure of generalized Orlicz-Lorentz spaces. Part II - Local stucture

A Note on the Maximal Operator in $L\sp{p(x)}$ (continuation)

Reduction theorems for weighted Hardy inequalities (the case 0 less than p less than or equal to 1)

On strict convergence in BV

On strict convergence in BV

Hardy inequality: negative exponents and connection to the spectrum of a differential operator

Hardy inequality: the spectrum of the Sturm-Liouville problem

Embeddings of Besov spaces (elementary approach)

Pictures and News from Miami (the Cwikel Conference and the AMS Meeting)

Some new results on restriction of Fourier multipliers

Weighted estimates for the averaging integral operator

Averages and optimality

Homeomorphisms with finite variation

Embeddings of Lorentz spaces

Traces and rearrangements

A simple proof of a theorem of Kerman and Pick

Quantitative Sobolev and Hardy inequalities

Traces and rearrangements

On boundedness of the Riesz potential in the local Morrey-type spaces

Gagliardo-Nirenberg inequalities in Orlicz spaces equipped with not necessarily doubling measures

Function Spaces with Varying Smoothness

Singular Integral Operators with Rough Kernels

Singular integral operators with rough kernels

Optimal good lambda inequalities

Improved Hardy-Sobolev inequalities

and

Besov spaces arising in connection with stochastic processes on fractals

Hardy-negative

Calderon type theorem for operators with non-standard endpoint behaviour

December 12

Interpolation characterization of the rearrangement-invariant hull of a Besov space

Estimates for the modulus of continuity of the Bessel potential and applications

On the interpolation theorems concerning B^p(R^n), BMO(R^n) and CMO^p(R^n)

Maximal Operator on L^{p(x)}

Besov spaces on metric spaces

Weighted Inequalities with Non-Standard Parameters:

2-microlocal Besov spaces

Extrapolation of compactness and its applications to Sobolev embeddings

On sharp embeddings of function spaces of generalized smoothness in L_1^loc

Trigonometric approximation and realizations of K-functionals

Trace operators in Besov and Triebel-Lizorkin spaces

Besov Spaces of Near Zero Smoothness

The Hundred Years of Sergey Lvovich Sobolev

Besov Spaces (survey)

Norms on grand and small Lebesgue spaces

Essential norms and localization moduli of Sobolev embeddings

The Fourier transform and function spaces

Rough and rougher singular integrals.

The Fourier transform and function spaces

The Fourier transform and function spaces

Littlewood-Payley theory and multipliers

Tangent distributions and Sobolev surfaces

Function spaces arising in connection with the Fourier transform

On trace spaces of function spaces with a radial weight (joint work with Dorothee Haroske)

Function spaces arising in connection with the Fourier transform

Litllewood-Paley Characterization of Lipschitz Spaces

On the boundedness of the maximal operator in generalized Morrey spaces

On the boundedness of the singular integral operators in generalized Morrey spaces

Weak-type estimates cannot be extrapolated

Monotone metric spaces

Linear and nonlinear equations with natural growth terms

In Orlicz spaces p-Amemiya norm is geometrically better than the Luxemburg and the Orlicz norms

Integral with a control function

Is the Trudinger-Moser nonlinearity a true critical nonlinearity?

Explicit formulas for optimal rearrangement-invariant norms in Sobolev imbedding inequalities

Optimality and iteration

Luzin-type theorem with convex integration and quasi-convex hulls of sets

Generalized trigonometric functions from different points of view

Optimality, iteration and isoperimetric problem

Sobolev homeomorphism with zero Jacobian

Optimality, iteration and isoperimetric problem

Hardy inequalities of higher order

On the zero modes of Pauli operators and inequalities of Hardy and Sobolev

Invertibility conditions for mappings of finite distortion

Optimality, iteration and isoperimetric problem

Maximal singular operators with rough kernels

Weak-type estimates for rough commutators

Boundedness of classical operators on classical Lorentz spaces

Composition operators on Sobolev-Orlicz spaces

Composition operators on Sobolev-Orlicz spaces

Compactness of higher-order Sobolev embeddings

Gelfand numbers (or widths) and compact linear operators in Banach spaces

Some phenomena in variable Lebesgue spaces theory

Inequalities for moduli of smoothness versus embeddings of function spaces

The Moser constant for a Trudinger-type embedding

Sobolev embedding with general underlying domains

Weighted inequalities for Hardy integral operators with variable boundaries and applications

The Moser constant for a Trudinger-type embedding

Boundedness of the clasical integral operators in general Morrey type spaces and some applications.

Marcinkiewicz interpolation theorems for Orlicz and Loretz gamma spaces

Compact interpolationon Besov-type and Triebel-Lizorkin-type spaces

Marcinkiewicz interpolation theorems for Orlicz and Loretz gamma spaces

Operators on cones of monotone functions

On the variation of the Hardy-Littlewood maximal function

Sobolev and bi-Sobolev homeomorphisms with zero Jacobian almost everywhere

Boundedness of spherical maximal function in variable L^p spaces and applications

On Sobolev embeddings in mixed norm spaces

On generalized Lorentz spaces

Convolution inequalities in weighted Lorentz spaces

On Sobolev embeddings in mixed norm spaces

Concentration-Compactness Principle for generalized Moser-Trudinger inequalities: characterization of the non-compactness in the radial case

Concentration-Compactness Principle for the Moser-Trudinger inequality: new proof of the Lions estimate

Concentration-Compactness Principle for the Moser-Trudinger inequality: characterization of the non-compactness in the radial case

Sobolev-type functions in metric spaces and their regularization: the Newtonian approach. (Lipschitz truncations as an application of weak boundedness of maximal operators.)

Concentration-Compactness Principle for the Moser-Trudinger inequality: characterization of the non-compactness in the radial case

Optimal Sobolev Trace Embeddings (joint work with Andrea Cianchi)

Regularity of Newtonian functions: quasicontinuity and continuity

Optimal Sobolev Trace Embeddings (joint work with Andrea Cianchi)

On the summability of quadratical and triangular partial sums of double Fourier series

Non-absolutely convergent integral in metric spaces

Non-absolutely convergent integral in metric spaces

Banach algebras of weakly-differentiable functions (joint work with Andrea Cianchi and Lenka Slavíková)

A Sobolev space embedded to L_infinity does not have to be a Banach algebra

Marcinkewicz theorem in L^p(x) spaces

Norms supporting the Lebesgue differentiation theorem (joint work with Paola Cavaliere, Andrea Cianchi and Luboš Pick)

Optimal Orlicz domains in Sobolev embeddings

On Peetre's maximal operator

On local means and Peetre's maximal operator

On local means and Peetre's maximal operator (theorem of Bui, Paluszyñski and Taibleson).

On local means and Peetre's maximal operator (theorem of Bui, Paluszyñski and Taibleson).

Mappings of finite distortion: Size of the branch set

Optimal rearrangement-invariant spaces for the Laplace transform

Some maximal inequalities.

Optimal Orlicz domains in Sobolev embeddings into Orlicz spaces.

Small sets of curves with respect to function spaces (joint work with Vendula Honzlová-Exnerová and Olli Martio)

The Wiener process and stochastic differential equations

Luzin condition and laminates

Small sets of curves with respect to function spaces (joint work with Vendula Honzlová-Exnerová and Olli Martio)

Minimal smoothness conditions for bilinear Fourier multipliers

Diffeomorphic approximation of planar elastic deformations

Necessity of bump conditions for the two-weighted maximal inequality

Mappings of finite distortion: integrability of the Jacobian

On the Aubin property of implicit multifunctions

On a continuous Rubik's cube br>

On the a.e. convergence and summability of series with respect to block-orthonormal systems

Images of porous sets under Sobolev mappings

Marchaud's theorem in infinite dimension

Sobolev homeomorphism in $W^{k,p}$ and the Lusin $(N)$ condition

Sobolev spaces and Lusin's condition (N) on hyperplanes

Mappings of finite distortion: size of the branch set (joint work with Chang-Yu Guo and Stanislav Hencl).

Embeddings and duals of Copson-Lorentz spaces

Optimality of function spaces for classical integral operators

Entropy numbers of Schatten classes

Approximation of monotone maps by diffeomorphisms

Sobolev extension domains: from the viewpoint of uniform domains.

Characterization of interpolation between grand, small, and classical Lebesgue spaces

Composition operator for functions of bounded variation

How not to leave traces

Filip Soudský (MFF UK Praha):

Emanuela Radici (FAU Erlangen-Nurnberg):

Luboš Pick (Charles University, Prague):

Filip Tomiæ (University of Novi Sad)

Properties of BLD-mappingsAbstract: We discuss several equivalent definitions for BLD-mappings between metric spaces and study their asymptotic values and limiting properties in the setting of Riemannian manifolds.

Rough maximal bilinear singular integrals

From functional inequalities to spectral properties of Schrödinger operators

Gelfand-Shilov spaces, Gevrey classes, and related topics

Gagliardo-Nirenberg interpolation inequality revisited.

Compactness of traces of Sobolev functions.

An optimal criterion for $L^2\times L^2 \to L^1$ boundedness.

Weak regularity of the inverse under minimal assumptions

Weak regularity of the inverse under minimal assumptions

INTERPOLATION BETWEEN HÖLDER AND LEBESGUE SPACES WITH APPLICATIONS

(joint work with Filip Soudský and Anastasia Molchanova)

Abstract:

Classical interpolation inequality of the type $\|u\|_X ≤ C\|u\|_Y^{\theta} \|u\|_ Z^\theta$ is well known in the case when $X, Y, Z$ are Lebesgue spaces. In this paper we show that this result may be extended by replacing norms $\|\cdot\|_Y$ or $\|\cdot\|_X$ by suitable Hölder semi-norm. We shall even prove sharper version involving weak Lorentz norm. We apply this result to prove the Gagliardo-Nirenberg inequality for a wider scale of parameters.

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