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

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.