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

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.

Version 4: 18 pages. Title and abstract have been changed. Minor cosmetic changes to paper

References in corpus (3)

• Dilations and rigid factorisations on noncommutative L^p-spaces
• On multiparameter Weighted ergodic theorem for Noncommutative L_{p}-spaces
• Noncommutative maximal strong $L_p$ estimates of Calderón-Zygmund operators