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Probability Theory and Related Fields

, Volume 152, Issue 1–2, pp 179–206 | Cite as

Interpolation and Φ-moment inequalities of noncommutative martingales

  • Turdebek N. Bekjan
  • Zeqian Chen
Article

Abstract

This paper is devoted to the study of Φ-moment inequalities for noncommutative martingales. In particular, we prove the noncommutative Φ-moment analogues of martingale transformations, Stein’s inequalities, Khintchine’s inequalities for Rademacher’s random variables, and Burkholder–Gundy’s inequalities. The key ingredient is a noncommutative version of Marcinkiewicz type interpolation theorem for Orlicz spaces which we establish in this paper.

Keywords

τ-Measurable operators Noncommutative martingale Interpolation Φ-Moment martingale inequality Noncommutative Orlicz space 

Mathematics Subject Classification (2000)

46L53 46L52 60G42 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.College of Mathematics and Systems ScienceXinjiang UniversityUrumqiChina
  2. 2.Wuhan Institute of Physics and MathematicsChinese Academy of SciencesWuhanChina

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