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

2025/08/07 by Yue Zhang, Zhang, Yue
Mathematics · #42B25 #46E40 #46L52 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2508.05718

openalex publication_date 2025/08/07 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish dimension-free estimates for the discrete spherical maximal operator on semi-commutative L_p space for 2≤ p≤∞.

Citations

• Noncommutative spherical maximal inequality associated with automorphisms
• Dimension-free estimates for the discrete spherical maximal functions
• Pointwise convergence of noncommutative Fourier series
• On discrete Hardy-Littlewood maximal functions over the balls in \mathbb Z^d: dimension-free estimates
• Singular integrals in quantum Euclidean spaces
• Noncommutative ergodic averages of balls and spheres over Euclidean spaces
• The discrete spherical averages over a family of sparse sequences
• Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori
• Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori
• On the Hardy-Littlewood maximal function for the cube
• Smooth Fourier multipliers on group von Neumann algebras
• Noncommutative maximal ergodic theorems
• Discrete analogues in harmonic analysis: Spherical averages
• Doob's inequality for non-commutative martingales

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• Dimension-free estimates for the discrete spherical maximal functions
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• L^p-improving bounds for spherical maximal operators over restricted dilation sets: radial improvement