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arXiv · 1108.2795

Noncommutative maximal inequalities associated with convex functions

Turdebek N. Bekjan·Zeqian Chen·Adam Osȩkowski
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Abstract

We prove several noncommutative maximal inequalities associated with convex functions, including a Doob type inequality for a convex function of maximal operators on noncommutative martingales, noncommutative Dunford-Schwartz and Stein maximal ergodic inequalities for a convex function of positive and symmetric positive contractions. The key ingredient in our proofs is a Marcinkiewicz type interpolation theorem for a convex function of maximal operators in the noncommutative setting, which we establish in this paper. These generalize the results of Junge and Xu in the $L^p$ case to the case of convex functions.

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Turdebek N. Bekjan, Zeqian Chen, Adam Osȩkowski. 2011-08-13. Noncommutative maximal inequalities associated with convex functions. https://arxiv.org/abs/1108.2795

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