Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 961502, 20 pages
doi:10.1155/2010/961502
Research Article

Commutators of Littlewood-Paley Operators on the Generalized Morrey Space

Yanping Chen,1 Yong Ding,2 and Xinxia Wang3

1Department of Mathematics and Mechanics, Applied Science School, University of Science and Technology Beijing, Beijing 100083, China
2Laboratory of Mathematics and Complex Systems (BNU), School of Mathematical Sciences, Beijing Normal University, Ministry of Education, Beijing 100875, China
3The College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China

Received 6 May 2010; Accepted 11 July 2010

Academic Editor: Shusen Ding

Copyright © 2010 Yanping Chen 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

Let μΩ, μSϖ, and μλ∗,ϖ denote the Marcinkiewicz integral, the parameterized area integral, and the parameterized Littlewood-Paley gλ∗ function, respectively. In this paper, the authors give a characterization of BMO space by the boundedness of the commutators of μΩ, μSϖ, and μλ∗,ϖ on the generalized Morrey space Lp,φ(ℝn).