Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents

DOI10.1080/17476933.2010.504837zbMath1228.31004OpenAlexW2093637675MaRDI QIDQ3093064

Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno, Tetsu Shimomura

Publication date: 12 October 2011

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2010.504837

zbMATH Keywords

Sobolev inequalityMorrey spaceRiesz potentialSobolev embeddingvariable exponentTrudinger's exponential inequality

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) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (38)

Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials ⋮ Trudinger's inequality and continuity for Riesz potentials of functions in grand Musielak-Orlicz-Morrey spaces over nondoubling metric measure spaces ⋮ A trace inequality of Riesz potentials in variable exponent Orlicz spaces ⋮ Sobolev-type inequalities on variable exponent Morrey spaces of an integral form ⋮ Sobolev's inequality in central Herz-Morrey-Musielak-Orlicz spaces over metric measure spaces ⋮ Sobolev and Trudinger type inequalities on grand Musielak-Orlicz-Morrey spaces ⋮ Generalized fractional integral operators on variable exponent Morrey spaces of an integral form ⋮ Sobolev embeddings for Riesz potentials of functions in Musielak–Orlicz–Morrey spaces over non-doubling measure spaces ⋮ Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces ⋮ Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents ⋮ Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces ⋮ Campanato-Morrey spaces for the double phase functionals with variable exponents ⋮ Sobolev's inequality for double phase functionals with variable exponents ⋮ Trudinger's inequality on Musielak-Orlicz-Morrey spaces over non-doubling metric measure spaces ⋮ Trudinger's inequality and continuity of potentials on Musielak-Orlicz-Morrey spaces ⋮ Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces ⋮ Sobolev type inequalities for fractional maximal functions and Riesz potentials in Morrey spaces of variable exponent on half spaces ⋮ Continuity of generalized Riesz potentials for double phase functionals with variable exponents over metric measure spaces ⋮ Biographical Sketch of Professor Eiichi Nakai ⋮ Sobolev's inequality for Musielak-Orlicz-Sobolev functions ⋮ Generalized fractional integral operators on variable exponent Morrey type spaces over metric measure spaces ⋮ Hardy-Littlewood-Sobolev theorem for variable Riesz potentials ⋮ Campanato-Morrey spaces for the double phase functionals ⋮ The Ahlfors–Beurling transform on Morrey spaces with variable exponents ⋮ Trudinger's inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces on metric measure spaces ⋮ Boundedness of maximal operator, Hardy operator and Sobolev's inequalities on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces ⋮ Continuity of generalized Riesz potentials for double phase functionals ⋮ Generalized fractional integrals on generalized Morrey spaces ⋮ Boundedness of fractional maximal operators for double phase functionals with variable exponents ⋮ Characterizations of some operators on the vanishing generalized Morrey spaces with variable exponent ⋮ Weak estimates for the maximal and Riesz potential operators in central Herz-Morrey spaces on the unit ball ⋮ Sobolev type inequalities for fractional maximal functions and Green potentials in half spaces ⋮ Herz–Morrey spaces of variable exponent, Riesz potential operator and duality ⋮ SOBOLEV’S INEQUALITY FOR MUSIELAK–ORLICZ–MORREY SPACES OVER METRIC MEASURE SPACES ⋮ Trudinger's inequality for double phase functionals with variable exponents ⋮ Sobolev-type inequalities on Musielak-Orlicz-Morrey spaces of an integral form ⋮ Weighted Morrey spaces of variable exponent and Riesz potentials ⋮ Continuity of generalized Riesz potentials for double phase functionals with variable exponents

Cites Work

• Continuity properties of Riesz potentials of Orlicz functions
• Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent
• A note on Riesz potentials
• On the theory of \({\mathcal L}_{p, \lambda}\) spaces
• Approximate identities and Young type inequalities in variable Lebesgue-Orlicz spaces Lp(.)(log L)q(.)
• The Campanato, Morrey and Hölder spaces on spaces of homogeneous type
• Orlicz–Morrey spaces and the Hardy–Littlewood maximal function
• 𝐿log𝐿 results for the maximal operator in variable 𝐿^{𝑝} spaces
• Weakly Differentiable Functions
• Hardy-Littlewood Maximal Operator, Singular Integral Operators and the Riesz Potentials on Generalized Morrey Spaces
• Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials

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