Dimension-free estimate for semi-commutative discrete spherical maximal operator

TL;DR

This paper proves that the discrete spherical maximal operator has bounds independent of dimension on semi-commutative Lp spaces for p between 2 and infinity, advancing understanding of harmonic analysis in non-commutative settings.

Contribution

It introduces dimension-free estimates for the discrete spherical maximal operator specifically on semi-commutative Lp spaces, a novel extension in harmonic analysis.

Findings

Established dimension-free bounds for the operator

Extended analysis to semi-commutative Lp spaces

Applicable for p in [2, infinity]

Abstract

In this paper, we establish dimension-free estimates for the discrete spherical maximal operator on semi-commutative $L_{p}$ space for $2\leq p\leq\infty$.