Divergent square averages

• 成果类型: Article
• 署名作者: Buczolich, Zoltan; Mauldin, R. Daniel
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 1479-1530
• 关键词: pointwise ergodic-theorems; quadratic residues

摘要

In this paper we answer a question of J. Bourgain which was motivated by questions A. Bellow and H. Furstenberg. We show that the sequence {n(2)}(n=1)(infinity) L-1-universally bad. This implies that it is not true that given a dynamical system. (X, Sigma, mu, T) and f is an element of L-1(mu), the ergodic means lim(N ->infinity) 1/N Sigma(N)(n=1) f(T-n2(x)) converge almost surely.