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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Noncommutative maximal inequalities associated with convex functions
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by Turdebek N. Bekjan, Zeqian Chen and Adam Osȩkowski PDF
Trans. Amer. Math. Soc. 369 (2017), 409-427 Request permission

Abstract:

We prove several noncommutative maximal inequalities associated with convex functions, including a Doob type inequality for a convex function of maximal operators on noncommutative martingales, and noncommutative Dunford-Schwartz and Stein maximal ergodic inequalities for a convex function of positive and symmetric positive contractions. The key ingredient in our proofs is a Marcinkiewicz type interpolation theorem for a convex function of maximal operators in the noncommutative setting, which we establish in this paper. These generalize the results of Junge and Xu in the $L^p$ case to the case of convex functions.
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Additional Information
  • Turdebek N. Bekjan
  • Affiliation: College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, People’s Republic of China
  • MR Author ID: 627291
  • Email: bek@xju.edu.cn
  • Zeqian Chen
  • Affiliation: Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, West District 30, Xiao-Hong-Shan, Wuhan 430071, People’s Republic of China
  • MR Author ID: 610740
  • Email: zqchen@wipm.ac.cn
  • Adam Osȩkowski
  • Affiliation: Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
  • ORCID: 0000-0002-8905-2418
  • Email: ados@mimuw.edu.pl
  • Received by editor(s): June 2, 2014
  • Received by editor(s) in revised form: December 30, 2014
  • Published electronically: February 24, 2016
  • Additional Notes: The first author was partially supported by NSFC grant No. 11371304
    The second author was partially supported by NSFC grant No. 11171338 and No. 11431011
    The third author was supported in part by MNiSW Grant N N201 364436
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 409-427
  • MSC (2010): Primary 46L53, 46L51
  • DOI: https://doi.org/10.1090/tran/6663
  • MathSciNet review: 3557778