CONVERGENCE OF WEIGHTED POLYNOMIAL MULTIPLE ERGODIC AVERAGES

被引：0

作者：

Chu, Qing ^{[1
]}

机构：

[1] Univ Paris Est, Lab Anal & Math Appl, CNRS, UMR 8050, F-77454 Marne La Vallee 2, France

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 04期

关键词：

Weighted ergodic averages; universally good sequences; Wiener-Wintner ergodic theorem; nilsequences; THEOREM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we study weighted polynomial multiple ergodic averages. A sequence of weights is called universally good if any polynomial multiple ergodic average with this sequence of weights converges in L(2). We find a necessary condition and show that for any bounded measurable function phi on an ergodic system, the sequence phi(T(n)x) is universally good for almost every x. The linear case was covered by Host and Kra.

引用

页码：1363 / 1369

页数：7

共 10 条

[1] Multiple recurrence and nilsequences [J].

Bergelson, V ;

Host, B ;

Kra, B ;

Ruzsa, I .

INVENTIONES MATHEMATICAE, 2005, 160 (02) :261-303

[2] Convergence of polynomial ergodic averages [J].

Host, B ;

Kra, B .

ISRAEL JOURNAL OF MATHEMATICS, 2005, 149 (1) :1-19

[3] Nonconventional ergodic averages and nilmanifolds [J].

Host, B ;

Kra, B .

ANNALS OF MATHEMATICS, 2005, 161 (01) :397-488

[4]

HOST B, UNIFORMITY SEMINORMS

[5] Convergence of multiple ergodic averages along polynomials of several variables [J].

Leibman, A .

ISRAEL JOURNAL OF MATHEMATICS, 2005, 146 (1) :303-315

[6] Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold [J].

Leibman, A .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 :201-213

[7]

LESIGNE E, 1993, ERGOD THEOR DYN SYST, V13, P767

[8] THEOREM OF DISJUNCTION OF DYNAMIC-SYSTEMS AND A GENERALIZATION O THE WIENER-WINTNER ERGODIC THEOREM [J].

LESIGNE, E .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1990, 10 :513-521

[9] Harmonic analysis and ergodic theory [J].

Wiener, N ;

Wintner, A .

AMERICAN JOURNAL OF MATHEMATICS, 1941, 63 :415-426

[10] A non-conventional ergodic theorem for a nilsystem [J].

Ziegler, T .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 :1357-1370

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