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arXiv · 2506.14431

Almost uniform convergence for noncommutative Vilenkin-Fourier series

Yong Jiao·Sijie Luo·Tiantian Zhao·Dejian Zhou
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Abstract

In the present paper, we study almost uniform convergence for noncommutative Vilenkin-Fourier series. Precisely, we establish several noncommutative (asymmetric) maximal inequalities for the Ces\`{a}ro means of the noncommutative Vilenkin-Fourier series, which in turn give the corresponding almost uniform convergence. The primary strategy in our proof is to explore a noncommutative generalization of Sunouchi square function operator, and the very recent advance of the noncommutative Calder\'{o}n-Zygmund decomposition.

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Yong Jiao, Sijie Luo, Tiantian Zhao, Dejian Zhou. 2025-06-17. Almost uniform convergence for noncommutative Vilenkin-Fourier series. https://arxiv.org/abs/2506.14431

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