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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 413716, 8 pages
http://dx.doi.org/10.1155/2014/413716
Research Article

Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces

1School of Computer Science and Technique, Henan Polytechnic University, Jiaozuo 454000, China
2School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

Received 10 December 2013; Accepted 18 May 2014; Published 1 June 2014

Academic Editor: Guozhen Lu

Copyright © 2014 Zhiheng Wang and Zengyan Si. 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 the infinitesimal generator of an analytic semigroup on with Gaussian kernel bounds, and let be the fractional integrals of for . For any locally integrable function , the commutators associated with are defined by . When (weighted space) or , the authors obtain the necessary and sufficient conditions for the boundedness of on weighted Morrey spaces, respectively.