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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