Maximal Function Methods for Sobolev Spaces

DOI10.1090/SURV/257zbMath1484.46002OpenAlexW3193844434MaRDI QIDQ3382174

Juha Kinnunen, Juha Lehrbäck, Antti V. Vähäkangas

Publication date: 20 September 2021

Published in: Mathematical Surveys and Monographs (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/surv/257

zbMATH Keywords

Sobolev spacescapacityPoincaré inequalityMuckenhoupt weightsmaximal functionsHardy's inequalitiesSobolev-Gagliardo-Nirenberg inequality$p$-Laplace equation

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Inequalities involving derivatives and differential and integral operators (26D10) Potentials and capacities, extremal length and related notions in higher dimensions (31B15) Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces (42-02) Quasilinear elliptic equations with (p)-Laplacian (35J92) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Harmonic analysis and PDEs (42B37)

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The Hajłasz capacity density condition is self-improving ⋮ Characterization of fractional Sobolev-Poincaré and (localized) Hardy inequalities ⋮ Self-improving properties of very weak solutions to double phase systems ⋮ A tribute to Pola Harboure: Isoperimetric inequalities and the HMS extrapolation theorem ⋮ Self-improving Poincaré-Sobolev type functionals in product spaces ⋮ A stability result for elliptic equations with singular nonlinearity and its applications to homogenization problems ⋮ The weighted Hardy constant ⋮ Higher integrability and stability of \((p,q)\)-quasiminimizers

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