Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 89396, 14 pages
doi:10.1155/JIA/2006/89396

Weighted estimates for commutators on nonhomogeneous spaces

Wengu Chen1 and Bing Zhao2

 1Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
2Beijing October First School, Beijing 100039, China
Received 14 November 2005; Revised 8 March 2006; Accepted 11 March 2006

Abstract

Let μ be a Borel measure on ℝd which may be nondoubling. The only condition that μ must satisfy is μ(Q)≤c0l(Q)n for any cube Q⊂ℝd with sides parallel to the coordinate axes and for some fixed n with 0<n≤d. This paper is to establish the weighted norm inequality for commutators of Calderón-Zygmund operators with RBMO(μ) functions by an estimate for a variant of the sharp maximal function in the context of the nonhomogeneous spaces.