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March 2021 Boundedness of maximal operator, Hardy operator and Sobolev’s inequalities on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces
Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura
Author Affiliations +
Hiroshima Math. J. 51(1): 13-55 (March 2021). DOI: 10.32917/h2019141

Abstract

Our aim in this paper is to deal with the boundedness of the Hardy- Littlewood maximal operator and the Hardy operator on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces and to establish a generalization of Sobolev’s inequalities for Riesz potentials of functions in such spaces.

Funding Statement

The third author is supported by Grant-in-Aid for Scientific Research(C), No. 19K03586.

Acknowledgement

We would like to express our thanks to the referee for his/her comments.

Citation

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Fumi-Yuki Maeda. Yoshihiro Mizuta. Takao Ohno. Tetsu Shimomura. "Boundedness of maximal operator, Hardy operator and Sobolev’s inequalities on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces." Hiroshima Math. J. 51 (1) 13 - 55, March 2021. https://doi.org/10.32917/h2019141

Information

Received: 25 December 2019; Revised: 12 January 2021; Published: March 2021
First available in Project Euclid: 19 April 2021

Digital Object Identifier: 10.32917/h2019141

Subjects:
Primary: 31B15
Secondary: 46E35

Keywords: Maximal operator , non-homogeneous central Herz-Morrey-Musielak- Orlicz spaces , Riesz potentials , Sobolev’s inequality

Rights: Copyright © 2021 Hiroshima University, Mathematics Program

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Vol.51 • No. 1 • 2021
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