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arXiv · 2302.04466

A noncommutative weak type maximal inequality for modulated ergodic averages with general weights

Morgan O'Brien
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Abstract

In this article, we prove a weak type $(p,p)$ maximal inequality, $1<p<\infty$, for weighted averages of a positive Dunford-Schwarz operator $T$ acting on a noncommutative $L_p$-space associated to a semifinite von Neumann algebra $\mathcal{M}$, with weights in $W_q$, where $\frac{1}{p}+\frac{1}{q}=1$. This result is then utilized to obtain modulated individual ergodic theorems with $q$-Besicovitch and $q$-Hartman sequences as weights. Multiparameter versions of these results are also investigated.

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Morgan O'Brien. 2023-02-09. A noncommutative weak type maximal inequality for modulated ergodic averages with general weights. https://doi.org/10.4064/cm9205-1-2024

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