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arXiv · 1506.04134

Noncommutative Burkholder/Rosenthal inequalities associated with convex functions

Narcisse Randrianantoanina·Lian Wu
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Abstract

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

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Narcisse Randrianantoanina, Lian Wu. 2015-06-12. Noncommutative Burkholder/Rosenthal inequalities associated with convex functions. https://arxiv.org/abs/1506.04134

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