Boundedness of Singular Integral Operators on Weak Herz Type Spaces with Variable Exponent

TL;DR

This paper introduces weak Herz spaces with variable exponents and proves the boundedness of various singular integral operators on these spaces, extending classical results to more general settings.

Contribution

It defines weak Herz and Hardy spaces with variable exponents and establishes boundedness results for singular integral operators within this framework.

Findings

Boundedness of singular integral operators on weak Herz spaces.

Extension of classical boundedness results to variable exponent spaces.

Introduction of weak Herz spaces with variable exponents.

Abstract

In this paper, the authors define the weak Herz spaces and the weak Herz-type Hardy spaces with variable exponent. As applications, the authors establish the boundedness for a large class of singular integral operators including some critical cases.