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# Marcinkiewicz Commutators with Lipschitz Functions in Non-homogeneous Spaces

Published:2011-07-04
Printed: Sep 2012
• Jiang Zhou,
College of Mathematics and Econometrics, Hunan University, ChangSha, 410082, P.R. China
• Bolin Ma,
College of Mathematics and Econometrics, Hunan University, ChangSha, 410082, P.R. China
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## Abstract

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: non doubling measure, Marcinkiewicz integral, commutator, ${\rm Lip}_{\beta}(\mu)$, $H^1(\mu)$
 MSC Classifications: 42B25 - Maximal functions, Littlewood-Paley theory 47B47 - Commutators, derivations, elementary operators, etc. 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.) 47A30 - Norms (inequalities, more than one norm, etc.)

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