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arXiv · 2211.09358

The sharp weighted maximal inequalities for noncommutative martingales

Tomasz Gałązka·Yong Jiao·Adam Osękowski·Lian Wu
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Abstract

The purpose of the paper is to establish weighted maximal $L_p$-inequalities in the context of operator-valued martingales on semifinite von Neumann algebras. The main emphasis is put on the optimal dependence of the $L_p$ constants on the characteristic of the weight involved. As applications, we establish weighted estimates for the noncommutative version of Hardy-Littlewood maximal operator and weighted bounds for noncommutative maximal truncations of a wide class of singular integrals.

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Tomasz Gałązka, Yong Jiao, Adam Osękowski, Lian Wu. 2022-11-17. The sharp weighted maximal inequalities for noncommutative martingales. https://arxiv.org/abs/2211.09358

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