Abstract and Applied Analysis
Volume 2008 (2008), Article ID 237937, 21 pages
doi:10.1155/2008/237937
Research Article

Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

Guoen Hu,1 Haibo Lin,2 and Dachun Yang2

1Department of Applied Mathematics, University of Information Engineering, P.O. Box 1001-747 Zhengzhou 450002, China
2School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received 20 August 2007; Revised 19 November 2007; Accepted 5 January 2008

Academic Editor: Yong Zhou

Copyright © 2008 Guoen Hu et al. 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

Weighted Lp for p∈(1,∞) and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.