Sharp maximal function inequalities and boundedness for commutators related to generalized fractional singular integral operators

Guangze Gu,Mingjie Cai

doi:10.1186/1029-242x-2014-211

Abstract

In this paper, some sharp maximal function inequalities for the commutators related to certain generalized fractional singular integral operators are proved. As an application, we obtain the boundedness of the commutators on Lebesgue, Morrey and Triebel-Lizorkin spaces.MSC:42B20, 42B25.

Highlights

Introduction and preliminariesLet b ∈ BMO(Rn) and T be the Calderón-Zygmund singular integral operator
By using a classical result of Coifman et al, we know that the commutator [b, T] is bounded on Lp(Rn) ( < 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 preliminariesLet b ∈ BMO(Rn) and T be the Calderón-Zygmund singular integral operator. 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.

Objectives

Results

Conclusion