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Marcinkiewicz Commutators with Lipschitz Functions in Non-homogeneous Spaces

Published online by Cambridge University Press:  20 November 2018

Jiang Zhou  and
Bolin Ma
Jiang Zhou
Affiliation:
College of Mathematics and Econometrics, Hunan University, ChangSha, 410082, P.R. ChinaandCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, P.R. Chinae-mail: zhoujiangshuxue@126.com
Bolin Ma
Affiliation:
College of Mathematics and Econometrics, Hunan University, ChangSha, 410082, P.R. ChinaandCollege of Mathematics and Engineering, Jiaxing University, Jiaxing, 314001, P.R. Chinae-mail: blma3030@yahoo.com.cn
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Abstract

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Under the assumption that $\mu $ is a nondoubling measure, we study certain commutators generated by the Lipschitz function and the Marcinkiewicz integral whose kernel satisfies a Hörmander-type condition. We establish the boundedness of these commutators on the Lebesgue spaces, Lipschitz spaces, and Hardy spaces. Our results are extensions of known theorems in the doubling case.

Keywords

42B2547B4742B2047A30non doubling measureMarcinkiewicz integralcommutatorLipβ(μ)H1(μ)
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 3 , 01 September 2012 , pp. 646 - 662
Copyright
Copyright © Canadian Mathematical Society 2012

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