Geodesic
Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 209-228.

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Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev's inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger's inequality and the continuity for Riesz potentials.
DOI : 10.1007/s10587-014-0095-8
Classification : 31B15, 46E35
Keywords: grand Morrey space; variable exponent; non-doubling measure; metric measure space; Riesz potential; maximal operator; Sobolev's inequality; Trudinger's exponential inequality; continuity 
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Ohno, Takao; Shimomura, Tetsu. Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 209-228. doi : 10.1007/s10587-014-0095-8. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0095-8/

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