Mixed radial-angular integrabilities for Hardy type operators

Ronghui Liu; Shuangping Tao

doi:10.4134/BKMS.b220726

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2023; 60(5): 1409-1425

Online first article September 5, 2023 Printed September 30, 2023

https://doi.org/10.4134/BKMS.b220726

Mixed radial-angular integrabilities for Hardy type operators

Ronghui Liu, Shuangping Tao

Northwest Normal University; Northwest Normal University

Abstract

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Abstract

In this paper, we are devoted to studying the mixed radial-angular integrabilities for Hardy type operators. As an application, the upper and lower bounds are obtained for the fractional Hardy operator. In addition, we also establish the sharp weak-type estimate for the fractional Hardy operator.

Keywords: Hardy type operator, fractional Hardy operator, mixed radial-angular integrability, weak-type estimate

MSC numbers: Primary 42B20; Secondary 42B25

Supported by: 202203101202) and the Young Teachers’ Scientific Research Ability Promotion Project of Northwest Normal University (NWNU-LKQN2023-15).