Almost uniform convergence for noncommutative Vilenkin-Fourier series
Functional Analysis
2025-06-18 v1
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.
Keywords
Cite
@article{arxiv.2506.14431,
title = {Almost uniform convergence for noncommutative Vilenkin-Fourier series},
author = {Yong Jiao and Sijie Luo and Tiantian Zhao and Dejian Zhou},
journal= {arXiv preprint arXiv:2506.14431},
year = {2025}
}
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35 pages