## Maximal operators of tree martingale transforms and their maximal operator inequalities

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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.## References

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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
- 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
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2434301