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Interpolation and Φ-moment inequalities of noncommutative martingales
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  • Published: 18 September 2010

Interpolation and Φ-moment inequalities of noncommutative martingales

  • Turdebek N. Bekjan1 &
  • Zeqian Chen2 

Probability Theory and Related Fields volume 152, pages 179–206 (2012)Cite this article

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  • 29 Citations

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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.

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Author information

Authors and Affiliations

  1. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, China

    Turdebek N. Bekjan

  2. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, West District 30, Xiao-Hong-Shan, Wuhan, 430071, China

    Zeqian Chen

Authors
  1. Turdebek N. Bekjan
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  2. Zeqian Chen
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Corresponding author

Correspondence to Zeqian Chen.

Additional information

T. Bekjan was partially supported by NSFC grant No. 10761009 and Z. Chen was partially supported by NSFC grant No. 10775175.

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Cite this article

Bekjan, T.N., Chen, Z. Interpolation and Φ-moment inequalities of noncommutative martingales. Probab. Theory Relat. Fields 152, 179–206 (2012). https://doi.org/10.1007/s00440-010-0319-2

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  • Received: 04 February 2010

  • Revised: 21 August 2010

  • Published: 18 September 2010

  • Issue Date: February 2012

  • DOI: https://doi.org/10.1007/s00440-010-0319-2

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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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