English

Khintchine inequalities and $Z_2$ sets

Functional Analysis 2025-03-06 v1

Abstract

In this paper we show that the subset of integers that satisfies the Khintchine inequality for p=1p=1 with the optimal constant 2{\sqrt{2}} has to be a Z2Z_2 set. We further prove a similar result for a large class of discrete groups. Our arguments rely on previous works by Haagerup/Musat \cite{Haagerup2007}, and Haagerup/Itoh \cite{Haagerup1995}.

Cite

@article{arxiv.2503.03187,
  title  = {Khintchine inequalities and $Z_2$ sets},
  author = {Chian Yeong Chuah and Zhen-Chuan Liu and Tao Mei},
  journal= {arXiv preprint arXiv:2503.03187},
  year   = {2025}
}
R2 v1 2026-06-28T22:07:21.196Z