2022 Hardy-Sobolev inequality in Herz spaces
Yoshihiro Mizuta, Tetsu Shimomura
Tohoku Math. J. (2) 74(2): 287-300 (2022). DOI: 10.2748/tmj.20210120b

Abstract

Our aim in this paper is to establish Hardy-Sobolev inequality in the settings of Herz spaces. As an application, we show Sobolev-type integral representation for a $C^1$-function on ${\mathbb R}^N \setminus \{0\}$ which vanishes outside the unit ball.

Citation

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Yoshihiro Mizuta. Tetsu Shimomura. "Hardy-Sobolev inequality in Herz spaces." Tohoku Math. J. (2) 74 (2) 287 - 300, 2022. https://doi.org/10.2748/tmj.20210120b

Information

Published: 2022
First available in Project Euclid: 6 July 2022

MathSciNet: MR4455869
zbMATH: 1504.46037
Digital Object Identifier: 10.2748/tmj.20210120b

Subjects:
Primary: 46E30
Secondary: 26D10 , 31B15

Keywords: generalized Riesz potentials , Hardy-Sobolev inequality , Herz spaces , Sobolev integral representation

Rights: Copyright © 2022 Tohoku University

Vol.74 • No. 2 • 2022
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