Tohoku Mathematical Journal
2022

June
SECOND SERIES VOL. 74, NO. 2

Tohoku Math. J.
74 (2022), 287-300

Title HARDY-SOBOLEV INEQUALITY IN HERZ SPACES

Author Yoshihiro Mizuta and Tetsu Shimomura

(Received September 16, 2020, revised January 18, 2021)
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.

Mathematics Subject Classification. Primary 46E30; Secondary 31B15, 26D10.

Key words and phrases. Hardy-Sobolev inequality, Herz spaces, generalized Riesz potentials, Sobolev integral representation.

To the top of this page

Back to the Contents