FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

DOI10.1017/S0004972709000343zbMath1176.42012MaRDI QIDQ3183150

Idha Sihwaningrum, Yoshihiro Sawano, Hendra Gunawan

Publication date: 19 October 2009

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

potential operatorsgeneralized Morrey spacesnon-doubling measurefractional integration operatorsolsen inequality

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Function spaces arising in harmonic analysis (42B35) Fractional derivatives and integrals (26A33) Integral operators (47G10) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items (12)

Bilinear fractional integral operators on Morrey spaces ⋮ Commutators of Calderón-Zygmund and generalized fractional integral operators on generalized Morrey spaces ⋮ 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 ⋮ Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operators ⋮ Compact commutators of Calderón-Zygmund and generalized fractional integral operators with a function in generalized Campanato spaces on generalized Morrey spaces ⋮ The local trace inequality for potential type integral operators ⋮ Some norm inequalities in Musielak-Orlicz spaces ⋮ Generalized fractional integrals on generalized Morrey spaces ⋮ Multilinear fractional integrals on Morrey spaces

Cites Work

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• Generalized Morrey spaces for non-doubling measures
• A note on Riesz potentials
• Some properties of fractional integrals. II
• The fall of the doubling condition in Calderón-Zygmund theory
• The \(Tb\)-theorem on non-homogeneous spaces.
• Boundedness properties of fractional integral operators associated to non-doubling measures
• Fractional Integration, morrey spaces and a schrödinger equation
• Boundedness of integral operators on generalized Morrey spaces and its application to Schrödinger operators
• Fractional Integrals and Generalized Olsen Inequalities

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