Compactness of commutators of multilinear singular integral operators with non-smooth kernels

TL;DR

This paper investigates the compactness of commutators of bilinear singular integral operators with non-smooth kernels on weighted Lebesgue spaces, introducing new maximal functions for analysis.

Contribution

It establishes the compactness of such commutators using novel maximal functions to control their behavior, advancing understanding of non-smooth kernel operators.

Findings

Proves compactness of commutators with non-smooth kernels

Introduces new maximal functions for analysis

Extends results to weighted Lebesgue spaces

Abstract

In this paper, the behavior for commutators of a class of bilinear singular integral operator associated with non-smooth kernels on the products of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO functions, compactness of the commutators is proved.