Interpolation and $Φ$-moment inequalities of noncommutative martingales

Details Interpolation and $Φ$-moment inequalities of noncommutative martingales Interpolation and $Φ$-moment inequalities of noncommutative martingales

2010-02-19

arxiv.org/abs/1002.3670v1

Probability Theory and Related Fields (2012) 152: 179-206

Mathematics

Operator Algebras

24 pages

Scientific paper

This paper is devoted to the study of $\Phi$-moment inequalities for noncommutative martingales. In particular, we prove the noncommutative $\Phi$-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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