Dimension-Free Estimates for Noncommutative Discrete Maximal Spherical Means

2025/11/17 by Gao, Li, Xu, Bang
#42B20 #46L51 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2511.13449

Abstract

In this paper, we establish dimension-free L_p-estimates for operator-valued maximal spherical means on cyclic groups \Z_m+1^d for all p>1 and m≥1. The key ingredient is a noncommutative extension of the spectral technique developed by Nevo and Stein. As an application, we obtain a noncommutative spherical maximal inequality for automorphism actions of von Neumann algebras.

Citations

• Dimension-free estimates for discrete maximal functions and lattice points in high-dimensional spheres and balls with small radii
• Noncommutative spherical maximal inequality associated with automorphisms
• A noncommutative maximal inequality for ergodic averages along arithmetic sets
• Noncommutative Stein's maximal spherical means
• Maximal singular integral operators acting on noncommutative L_p-spaces
• Interpolation of quasi noncommutative L_p-spaces
• Dimension-free Maximal Inequalities for Spherical Means in the Hypercube
• On the Hardy-Littlewood maximal function for the cube
• A reduction method for noncommutative L_p-spaces and applications
• Noncommutative maximal ergodic theorems
• Doob's inequality for non-commutative martingales

Related

• Noncommutative spherical maximal inequality associated with automorphisms
• Noncommutative Stein's maximal spherical means
• Noncommutative maximal ergodic theorems for spherical means on the\n Heisenberg group
• Dimension-free estimate for semi-commutative discrete spherical maximal operator
• Dimension-free Maximal Inequalities for Spherical Means in the Hypercube