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1 results

SOBOLEV’S INEQUALITY FOR MUSIELAK–ORLICZ–MORREY SPACES OVER METRIC MEASURE SPACES
Part of
- Linear function spaces and their duals
TAKAO OHNO, TETSU SHIMOMURA
Journal:

Journal of the Australian Mathematical Society / Volume 110 / Issue 3 / June 2021

Published online by Cambridge University Press:

02 October 2019, pp. 371-385

Print publication:

June 2021
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Our aim in this paper is to establish a generalization of Sobolev’s inequality for Riesz potentials $J_{\unicode[STIX]{x1D6FC}(\cdot )}^{\unicode[STIX]{x1D70E}}f$ of functions $f$ in Musielak–Orlicz–Morrey spaces $L^{\unicode[STIX]{x1D6F7},\unicode[STIX]{x1D705}}(X)$. As a corollary we obtain Sobolev’s inequality for double phase functionals with variable exponents.