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Displaying similar documents to “Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures”

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.

The fractional integral between weighted Orlicz and B M O φ spaces on spaces of homogeneous type

Gladis Pradolini, Oscar Salinas (2003)

Commentationes Mathematicae Universitatis Carolinae

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In this work we give sufficient and necessary conditions for the boundedness of the fractional integral operator acting between weighted Orlicz spaces and suitable B M O φ spaces, in the general setting of spaces of homogeneous type. This result generalizes those contained in [P1] and [P2] about the boundedness of the same operator acting between weighted L p and Lipschitz integral spaces on ℝ n . We also give some properties of the classes of pairs of weights appearing in connection with this...