Sharp Maximal Function Estimates and Boundedness for Commutator Related to Generalized Fractional Integral Operator

Guo Sheng; Huang Chuangxia; Liu Lanzhe

doi:10.2478/v10324-012-0018-z

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Sharp Maximal Function Estimates and Boundedness for Commutator Related to Generalized Fractional Integral Operator

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 50 (2012): Issue 2 (December 2012)

By: Guo Sheng, Huang Chuangxia and Liu Lanzhe

Open Access

|Jan 2013

Abstract

In this paper, we prove some sharp maximal function estimates for the commutators related to certain generalized fractional integral operator with general kernel and the BMO and Lipschitz functions. As an application, we obtain the boundedness of the commutators on Lebesgue, Morrey and Triebel-Lizorkin spaces. The operator includes fractional Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

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