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Journal of Function Spaces
Volume 2017, Article ID 3764142, 9 pages
https://doi.org/10.1155/2017/3764142
Research Article

Precompact Sets, Boundedness, and Compactness of Commutators for Singular Integrals in Variable Morrey Spaces

1School of Sciences, Central South University of Forestry and Technology, Changsha 410004, China
2Department of Mathematics, Hainan Normal University, Haikou 571158, China

Correspondence should be addressed to Jingshi Xu; moc.621@uxihsgnij

Received 10 May 2017; Accepted 18 June 2017; Published 20 July 2017

Academic Editor: Dashan Fan

Copyright © 2017 Wei Wang and Jingshi Xu. 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

We give sufficient conditions for subsets to be precompact sets in variable Morrey spaces. Then we obtain the boundedness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces. Finally, we discuss the compactness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces.