Oscillation and jump inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes

被引：1

作者：

Mehlhop, Nathan ^{[1
]}

Slomian, Wojciech ^{[2
,3
]}

机构：

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[2] BCAM Basque Ctr Appl Math, Bilbao 48009, Spain

[3] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Wyb Wyspianskiego 27, PL-50370 Wroclaw, Poland

来源：

MATHEMATISCHE ANNALEN | 2024年 / 388卷 / 03期

基金：

美国国家科学基金会;

关键词：

37A30 (Primary); 37A46; 42B20; THEOREM; PROOF;

D O I：

10.1007/s00208-023-02597-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the uniform oscillation and jump inequalities for the polynomial ergodic averages modeled over multi-dimensional subsets of primes. This is a contribution to the Rosenblatt-Wierdl conjecture (Lond Math Soc Lect Notes 205:3-151, 1995, Problem 4.12, p. 80) with averages taken over primes. These inequalities provide endpoints for the r-variational estimates obtained by Trojan (Math Ann 374:1597-1656, 2019).

引用

页码：2807 / 2842

页数：36