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Journal of Function Spaces
Volume 2015, Article ID 670649, 11 pages
Research Article

Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces

1School of Mathematical Sciences, Beijing Normal University, and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
2Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China
3Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, China

Received 28 July 2014; Accepted 29 October 2014

Academic Editor: Nelson José Merentes Díaz

Copyright © 2015 Sha He 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.


Let be the infinitesimal generator of an analytic semigroup on with Gaussian kernel bounds, and let be the fractional integrals of for . Assume that is a finite family of locally integrable functions; then the multilinear commutators generated by and are defined by . Assume that belongs to weighted BMO space, ; the authors obtain the boundedness of on weighted Morrey spaces. As a special case, when is the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutator on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results.