Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces

DOI10.1186/1029-242X-2013-12zbMath1279.31004WikidataQ59303041 ScholiaQ59303041MaRDI QIDQ389169

Tetsu Shimomura, Yoshihiro Sawano

Publication date: 17 January 2014

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

zbMATH Keywords

Sobolev inequalityRiesz potentialsnon-doubling measureMorrey spaces of variable exponents

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractional derivatives and integrals (26A33) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (10)

Generalized Morrey spaces and trace operator ⋮ Generalized fractional integral operators on generalized Orlicz-Morrey spaces of the second kind over non-doubling metric measure spaces ⋮ Boundedness of operators and inequalities on Morrey-Banach spaces ⋮ Definability of singular integral operators on Morrey-Banach spaces ⋮ The Ahlfors–Beurling transform on Morrey spaces with variable exponents ⋮ Extension of Hardy-Littlewood-Sobolev inequalities for Riesz potentials on hypergroups ⋮ Weak type inequalities for some integral operators on generalized nonhomogeneous Morrey spaces ⋮ A Thought on Generalized Morrey Spaces ⋮ Hardy spaces \(H^p\) over non-homogeneous metric measure spaces and their applications ⋮ SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN OVER NONDOUBLING MEASURE SPACES

Cites Work

• Unnamed Item
• Unnamed Item
• Orlicz-Morrey spaces and fractional operators
• Generalized Morrey spaces for non-doubling measures
• Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent
• Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent
• A note on Riesz potentials
• Morrey spaces for non-doubling measures
• On the theory of \({\mathcal L}_{p, \lambda}\) spaces
• Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents
• FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES
• Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure
• Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials

This page was built for publication: Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces