$\Phi$-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
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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