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SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN $L^{p(\cdot )}$ OVER NONDOUBLING MEASURE SPACES

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  12 November 2015

TAKAO OHNO  and
TETSU SHIMOMURA
TAKAO OHNO*
Affiliation:
Faculty of Education and Welfare Science, Oita University, Dannoharu Oita-city 870-1192, Japan email [email protected]
TETSU SHIMOMURA
Affiliation:
Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan email [email protected]
*
✉[email protected]
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Abstract

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Our aim in this paper is to deal with Sobolev inequalities for Riesz potentials of functions in Lebesgue spaces of variable exponents near Sobolev’s exponent over nondoubling metric measure spaces.

Keywords

Riesz potentialSobolev inequalityvariable exponentmetric measure spacenondoubling measure

MSC classification

Primary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Secondary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 128 - 136
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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