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

Voir la notice de l'article provenant de la source Cambridge University Press

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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