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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Commutators of weighted Hardy operators on $ \mathbb{R}^{n}$


Authors: Zun Wei Fu, Zong Guang Liu and Shan Zhen Lu
Journal: Proc. Amer. Math. Soc. 137 (2009), 3319-3328
MSC (2000): Primary 42B25; Secondary 26D15, 42B99
Published electronically: May 27, 2009
MathSciNet review: 2515401
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Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to establish a sufficient and necessary condition on weight functions which ensures the boundedness of the commutators of weighted Hardy operators (with symbols in BMO $ (\mathbb{R}^{n})$) on $ L^{p}(\mathbb{R}^{n})$, where $ 1<p<\infty$.


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Additional Information

Zun Wei Fu
Affiliation: Department of Mathematics, Linyi Normal University, Linyi Shandong, 276005, People’s Republic of China
Address at time of publication: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China
Email: lyfzw@tom.com

Zong Guang Liu
Affiliation: Department of Mathematics, China University of Mining and Technology (Beijing), Beijing, 100083, People’s Republic of China
Email: liuzg@cumtb.edu.cn

Shan Zhen Lu
Affiliation: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China
Email: lusz@bnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09824-4
PII: S 0002-9939(09)09824-4
Keywords: Weighted Hardy operator, BMO, commutator
Received by editor(s): May 20, 2008
Published electronically: May 27, 2009
Additional Notes: The first and third authors were supported in part by NSFC Grant #10871024.
The second author was supported in part by NSFC Grant #10371080.
The corresponding author should be Shan Zhen Lu.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2009 American Mathematical Society