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Maximal operators of tree martingale transforms and their maximal operator inequalities


Authors: Tong-jun He and Yi Shen
Journal: Trans. Amer. Math. Soc. 360 (2008), 6595-6609
MSC (2000): Primary 60G46, 46B09
DOI: https://doi.org/10.1090/S0002-9947-08-04502-9
Published electronically: July 28, 2008
MathSciNet review: 2434301
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Abstract: In this paper we define maximal operators for tree martingale transforms in $ {UMD}$ spaces and prove inequalities for them by using the $ {UMD}$ property.


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Additional Information

Tong-jun He
Affiliation: Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
Address at time of publication: College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, People’s Republic of China
Email: hetongjun@fzu.edu.cn

Yi Shen
Affiliation: Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
Email: lhfu@hust.edu.cn

DOI: https://doi.org/10.1090/S0002-9947-08-04502-9
Keywords: Tree martingale, $UMD$ spaces, maximal operator
Received by editor(s): August 28, 2006
Received by editor(s) in revised form: March 1, 2007
Published electronically: July 28, 2008
Additional Notes: The authors were partially supported by NSFC Grant: 60574025
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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