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arXiv · 2511.13449

Dimension-free maximal inequalities for noncommutative spherical means over cyclic groups

Li Gao·Bang Xu
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Abstract

In this paper, we establish dimension-free $L_p$-estimates for operator-valued maximal spherical means over cyclic groups $\Z_{m+1}^d$ for all $p>1$ and $m\geq1$. 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 on von Neumann algebras, along with several concrete examples.

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Li Gao, Bang Xu. 2025-11-17. Dimension-free maximal inequalities for noncommutative spherical means over cyclic groups. https://arxiv.org/abs/2511.13449

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