POINTWISE CONVERGENCE OF ERGODIC AVERAGES ALONG CUBES

被引：20

作者：

Assani, I. ^{[1
]}

机构：

[1] Univ N Carolina, Dept Math, Chapel Hill, NC 27599 USA

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2010年 / 110卷

关键词：

Measure Preserve; Bounded Sequence; Pointwise Convergence; Inverse Limit; Ergodic Average;

D O I：

10.1007/s11854-010-0006-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (X, B, mu, T) be a measure preserving system. We prove the pointwise convergence of ergodic averages along cubes of 2(k) - 1 bounded and measurable functions for all k. We show that this result can be derived from estimates about bounded sequences of real numbers and apply these estimates to establish the pointwise convergence of some weighted ergodic averages and ergodic averages along cubes for not necessarily commuting measure preserving transformations.

引用

页码：241 / 269

页数：29

共 17 条

[1] [Anonymous], 2003, Wiener Wintner ergodic theorems
[2] [Anonymous], 1974, PURE APPL MATH
[3] Assani I, 2007, CONTEMP MATH, V430, P1
[4] ASSANI I, 2003, POINTWISE CONVERGENC
[5] JOINT ERGODICITY AND MIXING
BEREND, D
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 1985, 45 : 255 - 284
[6] BERGELSON V, 2000, DESCRIPTIVE SET THEO, P31
[7] BOURGAIN J, 1990, J REINE ANGEW MATH, V404, P140
[8] Maximal multilinear operators
Demeter, Ciprian
Tao, Terence
Thiele, Christoph
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (09) : 4989 - 5042
[9] Convergence of multiple ergodic averages for some commuting transformations
Frantzikinakis, N
Kra, B
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 : 799 - 809
[10] Furstenberg H, 1996, OHIO ST U M, V5, P193

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