Riesz type potential operators in generalized grand Morrey spaces

Details Riesz type potential operators in generalized grand Morrey spaces Riesz type potential operators in generalized grand Morrey spaces

2012-04-10

arxiv.org/abs/1204.2208v1

Mathematics

Functional Analysis

arXiv admin note: text overlap with arXiv:1109.2550

Scientific paper

In this paper we introduce generalized grand Morrey spaces in the framework of quasimetric measure spaces, in the spirit of the so-called grand Lebesgue spaces. We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in generalized grand Morrey spaces to the corresponding boundedness in Morrey spaces, as a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator as well as the boundedness of Calder\'on-Zygmund potential type operators. Boundedness of Riesz type potential operators are also obtained in the framework of homogeneous and also in the nonhomogeneous case in generalized grand Morrey spaces.

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