Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent

DOI10.1016/j.bulsci.2009.09.004zbMath1192.46027OpenAlexW1997235170MaRDI QIDQ846344

Tetsu Shimomura, Takao Ohno, Yoshihiro Mizuta

Publication date: 9 February 2010

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2009.09.004

zbMATH Keywords

Sobolev embeddingsOrlicz spaceRiesz potentialvariable exponent

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 (13)

Compact embeddings for Sobolev spaces of two variable exponents ⋮ A trace inequality of Riesz potentials in variable exponent Orlicz spaces ⋮ Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces ⋮ Trudinger's inequality on Musielak-Orlicz-Morrey spaces over non-doubling metric measure spaces ⋮ Trudinger's inequality for Riesz potentials on Musielak-Orlicz spaces over metric measure spaces ⋮ Trudinger's inequality and continuity of potentials on Musielak-Orlicz-Morrey spaces ⋮ Hardy-Littlewood-Sobolev theorem for variable Riesz potentials ⋮ Trudinger's inequality for Riesz potentials of functions in Musielak-Orlicz spaces ⋮ Trudinger's inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces on metric measure spaces ⋮ SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN OVER NONDOUBLING MEASURE SPACES ⋮ Weighted norm inequalities for the maximal operator on L^p(·) over spaces of homogeneous type ⋮ Herz–Morrey spaces of variable exponent, Riesz potential operator and duality ⋮ Trudinger's inequality for double phase functionals with variable exponents

Cites Work

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• Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space \(L^{p(\cdot)}(\log L)^{q(\cdot)}\)
• Sobolev inequalities with variable exponent attaining the values 1 and \(n\)
• Continuity properties for logarithmic potentials of functions in Morrey spaces of variable exponent
• Continuity properties of Riesz potentials for functions in L^p(⋅) of variable exponent
• 𝐿log𝐿 results for the maximal operator in variable 𝐿^{𝑝} spaces
• Strong and Weak Type Inequalities for Some Classical Operators in Orlicz Spaces
• On Certain Convolution Inequalities
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• Fractional Integration in Orlicz Spaces. I

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