<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

Department of Mathematics Changsha University of Science and Technology

Annals of West University of Timisoara - Mathematics and Computer Science

In this paper, we prove some sharp maximal function estimates for the commutators related to certain generalized fractional integral operator with general...

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

Published Online: Jan 15, 2013

Page range: 97 - 115

DOI: https://doi.org/10.2478/v10324-012-0018-z

Keywords
Commutator, Littlewood-Paley operator, Marcinkiewicz operator, Bochner-Riesz operator, Sharp maximal function, Morrey space, Triebel-Lizorkin space, BMO, Lipschitz function.

This content is open access.

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

Published Online: Jan 15, 2013

Page range: 97 - 115

DOI: https://doi.org/10.2478/v10324-012-0018-z

KeywordsCommutator, Littlewood-Paley operator, Marcinkiewicz operator, Bochner-Riesz operator, Sharp maximal function, Morrey space, Triebel-Lizorkin space, BMO, Lipschitz function.

This content is open access.

Keywords
Commutator, Littlewood-Paley operator, Marcinkiewicz operator, Bochner-Riesz operator, Sharp maximal function, Morrey space, Triebel-Lizorkin space, BMO, Lipschitz function.