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Maximal Inequalities of Noncommutative Martingale Transforms

Part of: Stochastic processes Selfadjoint operator algebras

Published online by Cambridge University Press:  22 November 2019

Yong Jiao ,
Fedor Sukochev  and
Dejian Zhou
Yong Jiao
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha410083, China Email: jiaoyong@csu.edu.cn
Fedor Sukochev
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Kensington2052, Australia Email: f.sukochev@unsw.edu.au
Dejian Zhou*
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha410083, China Email: zhoudejian@csu.edu.cn
*
* Email: zhoudejian@csu.edu.cn
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Abstract

In this paper, we investigate noncommutative symmetric and asymmetric maximal inequalities associated with martingale transforms and fractional integrals. Our proofs depend on some recent advances on algebraic atomic decomposition and the noncommutative Gundy decomposition. We also prove several fractional maximal inequalities.

Keywords

noncommutative martingalemaximal inequalitiesmartingale transformfractional integral

MSC classification

Primary: 46L53: Noncommutative probability and statistics
Secondary: 60G42: Martingales with discrete parameter 46L52: Noncommutative function spaces 60G46: Martingales and classical analysis
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 1 , February 2021 , pp. 221 - 248
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

Yong Jiao is supported by NSFC(11471337, 11722114).

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