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Journal of Function Spaces and Applications
Volume 2013, Article ID 410305, 11 pages
http://dx.doi.org/10.1155/2013/410305
Research Article

Endpoint Estimates for Generalized Commutators of Hardy Operators on Space

1Department of Mathematics, Shangrao Normal University, Shangrao City 334001, China
2Department of Mathematics, Zhejiang University, Hangzhou City 310027, China
3School of Mathematical Science, Beijing Normal University, Beijing City 100875, China

Received 25 March 2013; Accepted 7 May 2013

Academic Editor: Dashan Fan

Copyright © 2013 Xiao Yu and Shanzhen Lu. 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 study the -boundedness of the generalized commutators of Hardy operator with a homogeneous kernel as follows: , where with , and . We prove that, when , is not bounded from to unless . Finally, we prove that is bounded from to with .