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Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 2 / June 2020
- Published online by Cambridge University Press:
- 06 September 2019, pp. 287-303
- Print publication:
- June 2020
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- Article
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Our aim in this paper is to establish a generalization of Sobolev’s inequality for Riesz potentials
$I_{\unicode[STIX]{x1D6FC}(\,\cdot \,),\unicode[STIX]{x1D70F}}f$ of order 
$\unicode[STIX]{x1D6FC}(\,\cdot \,)$ with 
$f\in L^{\unicode[STIX]{x1D6F7},\unicode[STIX]{x1D705},\unicode[STIX]{x1D703}}(X)$ over bounded non-doubling metric measure spaces. As a corollary we obtain Sobolev’s inequality for double phase functionals with variable exponents.
