Polynomial averages and pointwise ergodic theorems on nilpotent groups

• 成果类型: Article
• 署名作者: Ionescu, Alexandru D.; Magyar, Akos; Mirek, Mariusz; Szarek, Tomasz Z.
• 署名单位: Princeton University; University System of Georgia; University of Georgia; Rutgers University System; Rutgers University New Brunswick; University of Wroclaw; Basque Center for Applied Mathematics (BCAM)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01159-0
• 发表日期: 2023
• 页码: 1023-1140
• 关键词: jump inequalities; radon transforms; norm convergence; harmonic-analysis; discrete analogs; PROOF

摘要

We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on sigma-finite measure spaces. We also establish corresponding maximal inequalities on Lp for 1 <=infinity and rho-variational inequalities on L2 for 2