Dimension-free estimates for semi-commutative discrete Hardy-Littlewood maximal operators

TL;DR

This paper proves that certain maximal operators in semi-commutative $L_p$ spaces have bounds independent of dimension, leading to new ergodic inequalities and convergence results.

Contribution

It establishes the first dimension-free $L_p$ bounds for discrete Hardy-Littlewood maximal operators in semi-commutative spaces for large radii.

Findings

Dimension-free $L_p$ bounds for large radii

Maximal ergodic inequalities derived

Bilateral almost uniform convergence proven

Abstract

For $2\leq p\leq \infty$, we establish dimension-free estimates for discrete dyadic Hardy-Littlewood maximal operators over Euclidean balls on semi-commutative $L_{p}$ space. In particular, when the radius is sufficiently large, these operators admit dimension-free $L_{p}$ bounds for all $1<p<\infty$. As applications, we derive the corresponding maximal ergodic inequalities and the bilaterally almost uniform convergence.