Noncommutative Burkholder/Rosenthal inequalities associated with convex functions

Abstract

We prove noncommutative martingale inequalities associated with convex functions. More precisely, we obtain $\Phi$-moment analogues of the noncommutative Burkholder inequalities and the noncommutative Rosenthal inequalities for any convex Orlicz function $\Phi$ whose Matuzewska-Orlicz indices $p_{\Phi }$ and $q_{\Phi }$ are such that $1<p_{\Phi }\le q_{\Phi }<2$ or $2<p_{\Phi }\le q_{\Phi }<\infty$. These results generalize the noncommutative Burkholder/Rosenthal inequalities due to Junge and Xu.

Cited by in corpus (1)

• Johnson-Schechtman and Khinchine inequalities in noncommutative probability theory