Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form

DOI10.1002/mana.200710122zbMath1211.46026OpenAlexW2056327291MaRDI QIDQ2786309

Yoshihiro Mizuta, Tetsu Shimomura

Publication date: 21 September 2010

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200710122

zbMATH Keywords

maximal functionfractional integralsMorrey spacesRiesz potentialHardy-Littewood-Sobolev inequalities

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) Maximal functions, Littlewood-Paley theory (42B25) Potential operators (47G40)

Related Items (13)

Sobolev-type inequalities on variable exponent Morrey spaces of an integral form ⋮ Generalized fractional integral operators on variable exponent Morrey spaces of an integral form ⋮ On Sobolev-type inequalities on Morrey spaces of an integral form ⋮ Trudinger's inequality on Musielak-Orlicz-Morrey spaces over non-doubling metric measure spaces ⋮ Sobolev's inequality in Musielak–Orlicz–Morrey spaces of an integral form ⋮ Trudinger's inequality and continuity of potentials on Musielak-Orlicz-Morrey spaces ⋮ Sobolev embeddings in grand Morrey spaces ⋮ Generalized fractional integral operators on variable exponent Morrey type spaces over metric measure spaces ⋮ Trudinger's inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces on metric measure spaces ⋮ Weighted fractional and Hardy type operators in Orlicz–Morrey spaces ⋮ On Trudinger-type Inequalities in Orlicz-Morrey Spaces of an Integral Form ⋮ Sobolev-type inequalities on Musielak-Orlicz-Morrey spaces of an integral form ⋮ Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form

Cites Work

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• Continuity properties of Riesz potentials of Orlicz functions
• Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent
• Vanishing exponential integrability for Riesz potentials of functions in Orlicz classes
• Continuity properties of potentials and Beppo-Levi-Deny functions
• Exponential integrability for Riesz potentials of functions in Orlicz classes
• Differentiability properties of Orlicz-Sobolev functions
• Über konjugierte Exponentenfolgen
• On Certain Convolution Inequalities
• Continuity properties for Riesz potentials of functions in Morrey spaces of variable exponent

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