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Journal of Function Spaces
Volume 2015, Article ID 548165, 12 pages
http://dx.doi.org/10.1155/2015/548165
Research Article

Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received 10 October 2015; Accepted 30 November 2015

Academic Editor: Henryk Hudzik

Copyright © 2015 Guanghui Lu and Shuangping Tao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a metric measure space satisfying the upper doubling condition and geometrically doubling condition in the sense of Hytönen. The aim of this paper is to establish the boundedness of commutator generated by the Marcinkiewicz integral and Lipschitz function . The authors prove that is bounded from the Lebesgue spaces to weak Lebesgue spaces for , from the Lebesgue spaces to the spaces for , and from the Lebesgue spaces to the Lipschitz spaces for . Moreover, some results in Morrey spaces and Hardy spaces are also discussed.