On the weighted Rellich-Sobolev and Hardy-Sobolev inequalities in variable exponent Lebesgue spaces

MaRDI QIDQ6579354

D. E. Edmunds, Alexander Meskhi

Publication date: 25 July 2024

Published in: Transactions of A. Razmadze Mathematical Institute (Search for Journal in Brave)

zbMATH Keywords

Hardy inequalityRellich inequalityvariable exponent Lebesgue spaceshomogeneous groupsweighted Sobolev inequality

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Analysis on real and complex Lie groups (22E30) Linear operators on function spaces (general) (47B38) Analysis on other specific Lie groups (43A80) Inequalities involving derivatives and differential and integral operators (26D10)

Cites Work

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• Quantization on nilpotent Lie groups
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• Lebesgue and Sobolev spaces with variable exponents
• Explicit constants for Rellich inequalities in \(L_p(\Omega)\)
• On the Rellich inequality in \(L^{p(\cdot)}(a,b)\)
• Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups
• Function spaces with variable exponents -- an introduction
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Hardy type inequality in variable Lebesgue spaces
• The boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous type
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• Two-weighted Hardy operators in $L^{p(\cdot )}$ spaces and applications

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