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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$\Phi$-moment inequalities for noncommutative differentially subordinate martingales
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by Yong Jiao, Mohammad Sal Moslehian, Lian Wu and Yahui Zuo;
Proc. Amer. Math. Soc. 152 (2024), 3551-3564
DOI: https://doi.org/10.1090/proc/16847
Published electronically: June 21, 2024

Abstract:

We establish some $\Phi$-moment inequalities for noncommutative differentially subordinate martingales. Let $\Phi$ be a $p$-convex and $q$-concave Orlicz function with $1<p\leq q<2$. Suppose that $x$ and $y$ are two self-adjoint martingales such that $y$ is weakly differentially subordinate to $x$. We show that, for $N\geq 0$, \begin{equation*} \tau \big [\Phi (|y_N|)\big ]\leq c_{p,q}\tau \big [\Phi (|x_N|)\big ], \end{equation*} where the constant $c_{p,q}$ is of the best order when $p=q$. The $\Phi$-moment estimates for square functions of noncommutative differentially subordinate martingales are also obtained in this article. Our approach provides constructive proofs of noncommutative $\Phi$-moment Burkholder–Gundy inequalities and Burkholder inequalities.
References
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Bibliographic Information
  • Yong Jiao
  • Affiliation: School of Mathematics and Statistics, Central South University, Changsha 410075, People’s Republic of China
  • MR Author ID: 828053
  • Email: jiaoyong@csu.edu.cn
  • Mohammad Sal Moslehian
  • Affiliation: Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran
  • MR Author ID: 620744
  • ORCID: 0000-0001-7905-528X
  • Email: moslehian@um.ac.ir
  • Lian Wu
  • Affiliation: School of Mathematics and Statistics, Central South University, Changsha 410075, People’s Republic of China
  • Email: wulian@csu.edu.cn
  • Yahui Zuo
  • Affiliation: School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, People’s Republic of China
  • MR Author ID: 1235518
  • Email: yahuizuo@xtu.edu.cn
  • Received by editor(s): August 11, 2023
  • Received by editor(s) in revised form: February 9, 2024, and March 3, 2024
  • Published electronically: June 21, 2024
  • Additional Notes: The first author was supported by the NSFC (No. 12125109). The third author was supported by the NSFC (No. 11971484).
    The fourth author is the corresponding author.
  • Communicated by: Zhen-Qing Chen
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3551-3564
  • MSC (2020): Primary 46L53, 60G42, 60G46
  • DOI: https://doi.org/10.1090/proc/16847
  • MathSciNet review: 4767283