Singular and fractional integral operators with variable kernels on the weak Hardy spaces

TL;DR

This paper investigates the boundedness of certain integral operators with variable kernels on weak Hardy spaces, using decomposition theorems and Dini conditions to establish key properties.

Contribution

It introduces new boundedness results for integral operators with variable kernels on weak Hardy spaces under Dini-type conditions.

Findings

Boundedness of integral operators with variable kernels established

Conditions under which operators are bounded on weak Hardy spaces identified

Extension of classical results to variable kernel setting

Abstract

In this paper, by using the decomposition theorem for weak Hardy spaces, we will obtain the boundedness properties of some integral operators with variable kernels on these spaces, under some Dini type conditions imposed on the variable kernel $\Omega(x,z)$.