Interpolation and $\Phi$-moment inequalities of noncommutative martingales

TL;DR

This paper develops noncommutative $\

Contribution

It introduces a noncommutative Marcinkiewicz interpolation theorem and extends classical inequalities to the noncommutative martingale setting.

Findings

Established noncommutative $\

Proved $\

Abstract

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.