Geodesic
Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces
Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 287-303

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DOI

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.
DOI : 10.4153/S0008439519000286
Mots-clés : maximal function, Riesz potential, Musielak–Orlicz–Morrey space, Sobolev’s inequality, metric measure space, non-doubling measure, double phase functional 
Ohno, Takao; Shimomura, Tetsu. Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces. Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 287-303. doi: 10.4153/S0008439519000286
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     author = {Ohno, Takao and Shimomura, Tetsu},
     title = {Sobolev{\textquoteright}s {Inequality} for {Riesz} {Potentials} of {Functions} in {Musielak{\textendash}Orlicz{\textendash}Morrey} {Spaces} {Over} {Non-doubling} {Metric} {Measure} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {287--303},
     year = {2020},
     volume = {63},
     number = {2},
     doi = {10.4153/S0008439519000286},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000286/}
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