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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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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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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DOI: https://doi.org/10.1007/s00440-010-0319-2
Keywords
- τ-Measurable operators
- Noncommutative martingale
- Interpolation
- Φ-Moment martingale inequality
- Noncommutative Orlicz space
Mathematics Subject Classification (2000)
- 46L53
- 46L52
- 60G42