Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces

Takao Ohno; Tetsu Shimomura

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 1, page 209-228
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Ohno, Takao, and Shimomura, Tetsu. "Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces." Czechoslovak Mathematical Journal 64.1 (2014): 209-228. <http://eudml.org/doc/261984>.

@article{Ohno2014,
abstract = {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.},
author = {Ohno, Takao, Shimomura, Tetsu},
journal = {Czechoslovak Mathematical Journal},
keywords = {grand Morrey space; variable exponent; non-doubling measure; metric measure space; Riesz potential; maximal operator; Sobolev's inequality; Trudinger's exponential inequality; continuity; grand Morrey space; variable exponent; non-doubling measure; metric measure space; Riesz potential; maximal operator; Sobolev's inequality; Trudinger's exponential inequality; continuity},
language = {eng},
number = {1},
pages = {209-228},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces},
url = {http://eudml.org/doc/261984},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Ohno, Takao
AU - Shimomura, Tetsu
TI - Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 209
EP - 228
AB - 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.
LA - eng
KW - grand Morrey space; variable exponent; non-doubling measure; metric measure space; Riesz potential; maximal operator; Sobolev's inequality; Trudinger's exponential inequality; continuity; grand Morrey space; variable exponent; non-doubling measure; metric measure space; Riesz potential; maximal operator; Sobolev's inequality; Trudinger's exponential inequality; continuity
UR - http://eudml.org/doc/261984
ER -

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