ON SERIES Σ ckf(kx) AND KHINCHIN'S CONJECTURE

被引：9

作者：

Berkes, Istvan ^{[1
]}

Weber, Michel ^{[2
]}

机构：

[1] Graz Univ Technol, Inst Stat, A-8010 Graz, Austria

[2] IRMA, F-67084 Strasbourg, France

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2014年 / 201卷 / 02期

基金：

奥地利科学基金会;

关键词：

CONVERGENCE;

D O I：

10.1007/s11856-014-0036-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the optimality of a criterion of Koksma (1953) in Khinchin's conjecture on strong uniform distribution. This verifies a claim of Bourgain (1988) and leads also to a near optimal a.e. convergence condition for series Sigma(infinity)(k=1) c(k)f(kx) with f is an element of L-2. Finally, we show that under mild regularity conditions on the Fourier coefficients of f, the Khinchin conjecture is valid assuming only f is an element of L-2.

引用

页码：593 / 609

页数：17

共 24 条

[1]

Aistleitner C, 2012, P AM MATH SOC, V140, P3893

[2]

Alexits G., 1961, CONVERGENCE PROBLEMS

[3]

[Anonymous], Q J MATH IN PRESS

[4]

[Anonymous], 1951, J INDIAN MATH SOC

[5]

[Anonymous], 1953, B SOC MATH BELG

[6]

[Anonymous], 1968, MAT ZAMETKI

[7]

[Anonymous], 1966, MAT SB

[8]

[Anonymous], ARXIV12100741V3MATHN

[9] On the convergence of Sigma c(n)f(nx) and the Lip 1/2 class [J].

Berkes, I .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (10) :4143-4158

[10]

Berkes I, 2009, MEM AM MATH SOC, V201, P1

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