Sharp function estimates and boundedness for commutators associated with general singular integral operator

Jiasheng Zeng

doi:10.1186/1029-242x-2014-108

Abstract

In this paper, we establish the sharp maximal function estimates for the commutator associated with the singular integral operator with general kernel. As an application, we obtain the boundedness of the commutator on weighted Lebesgue, Morrey, and Triebel-Lizorkin spaces.

Highlights

Introduction and preliminariesAs the development of singular integral operators, their commutators have been well studied
In [ – ], the authors prove that the commutators generated by the singular integral operators and BMO functions are bounded on Lp(Rn) for < p < ∞
In [ – ], the boundedness for the commutators generated by the singular integral operators and Lipschitz functions on Triebel-Lizorkin and Lp(Rn) ( < p < ∞) spaces are obtained

Summary

Introduction

Introduction and preliminariesAs the development of singular integral operators (see [ – ]), their commutators have been well studied. In [ – ], the authors prove that the commutators generated by the singular integral operators and BMO functions are bounded on Lp(Rn) for < p < ∞.

Objectives

Results

Conclusion