Sobolev embeddings for variable exponent Riesz potentials on metric spaces.

Futamura, Toshihide; Mizuta, Yoshihiro; Shimomura, Tetsu

Displaying similar documents to “Sobolev embeddings for variable exponent Riesz potentials on metric spaces.”

Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces

Takao Ohno, Tetsu Shimomura (2014)

Czechoslovak Mathematical Journal

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Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev's inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger's inequality and the continuity for Riesz potentials.

Sharp generalized Trudinger inequalities via truncation for embedding into multiple exponential spaces

Robert Černý (2010)

Commentationes Mathematicae Universitatis Carolinae

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We prove that the generalized Trudinger inequality for Orlicz-Sobolev spaces embedded into multiple exponential spaces implies a version of an inequality due to Brézis and Wainger.

Double exponential integrability, Bessel potentials and embedding theorems

David Edmunds, Petr Gurka, Bohumír Opic (1995)

Studia Mathematica

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This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.