Pointwise inequalities in variable Sobolev spaces and applications

DOI10.4171/ZAA/1317zbMath1131.46022OpenAlexW2055615269MaRDI QIDQ2454950

Alexandre Almeida, Stefan G. Samko

Publication date: 22 October 2007

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1317

zbMATH Keywords

Sobolev spacehypersingular integralHölder spaceSobolev embeddingvariable exponent

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractional derivatives and integrals (26A33) Inequalities involving derivatives and differential and integral operators (26D10)

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Cites Work

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• The fractional maximal operator and fractional integrals on variable \(L^p\) spaces
• Characterization of Riesz and Bessel potentials on variable Lebesgue spaces
• Maximal functions on Musielak--Orlicz spaces and generalized Lebesgue spaces
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• Density of smooth functions in W ^{k, p(x)} ( Ω )
• Calderón-Zygmund operators on generalized Lebesgue spaces Lp(⋅) and problems related to fluid dynamics
• Sobolev embeddings with variable exponent
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)

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