A Note on Boundedness of Singular Integral Operators on Function Spaces over Local Fields

TL;DR

This paper investigates the boundedness of classical singular integral operators with rough kernels over local fields, relaxing smoothness conditions to understand their behavior on various function spaces.

Contribution

It introduces new boundedness results for singular integral operators with less smooth kernels on different function spaces over local fields.

Findings

Established boundedness under relaxed kernel smoothness conditions

Extended classical results to rough kernel settings

Provided new criteria for operator boundedness on local field function spaces

Abstract

In this article we consider the classical singular integral operator over a local field with rough kernels. We study the boundedness of such an operator on different function spaces by relaxing the smoothness condition on kernels.