Weighted Sobolev inequality in Musielak-Orlicz space

DOI10.1016/J.JMAA.2011.10.055zbMath1243.46020OpenAlexW2044446292MaRDI QIDQ662051

Yoshihiro Mizuta, Tetsu Shimomura

Publication date: 11 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.10.055

zbMATH Keywords

Sobolev inequalityRiesz potentialMusielak-Orlicz spaces with variable exponents

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30)

Related Items (10)

New fractional maximal operators in the theory of martingale Hardy and Lebesgue spaces with variable exponents ⋮ Characterization of Lipschitz space via the commutators of fractional maximal functions on variable Lebesgue spaces ⋮ Hardy-Littlewood-Sobolev theorem for variable Riesz potentials ⋮ Variable exponent weighted norm inequality for generalized Riesz potentials ⋮ Rearrangement and the weighted logarithmic Sobolev inequality ⋮ Generalized fractional integrals on generalized Morrey spaces ⋮ Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball ⋮ Optimal estimates for the fractional Hardy operator on variable exponent Lebesgue spaces ⋮ Weighted Morrey spaces of variable exponent and Riesz potentials ⋮ Sobolev's inequality for Riesz potentials in Lorentz spaces of variable exponent

Cites Work

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• Hardy's inequality in Orlicz-Sobolev spaces of variable exponent
• Orlicz spaces and modular spaces
• Continuity properties of Riesz potentials of Orlicz functions
• Local-to-global results in variable exponent spaces
• Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space \(L^{p(\cdot)}(\log L)^{q(\cdot)}\)
• Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent
• Maximal functions on Musielak--Orlicz spaces and generalized Lebesgue spaces
• Weighted Sobolev theorem in Lebesgue spaces with variable exponent
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• Approximate identities and Young type inequalities in variable Lebesgue-Orlicz spaces Lp(.)(log L)q(.)
• Orlicz–Morrey spaces and the Hardy–Littlewood maximal function
• SOBOLEV INEQUALITIES FOR ORLICZ SPACES OF TWO VARIABLE EXPONENTS
• 𝐿log𝐿 results for the maximal operator in variable 𝐿^{𝑝} spaces
• On Certain Convolution Inequalities
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• Weighted Norm Inequalities for the Hardy Maximal Function

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