Trigonometric series with general monotone coefficients

被引：113
作者：
Tikhonov, S. [1 ]
机构：
[1] CRM, E-08193 Barcelona, Spain
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 326卷 / 01期
关键词：
trigonometric series; convergence; Hardy-Littlewood theorem;
D O I：
10.1016/j.jmaa.2006.02.053
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study trigonometric series with general monotone coefficients. Convergence results in the different metrics are obtained. Also, we prove a Hardy-type result on the behavior of the series near the origin. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：721 / 735
页数：15
相关论文
共 35 条
[1]  
[Anonymous], 1967, INTEGRABILITY THEORE
[2]   A new class of numerical sequences and its applications to sine and cosine series [J].
Leindler L. .
Analysis Mathematica, 2002, 28 (4) :279-286
[3]   INTEGRABILITY THEOREMS FOR FOURIER SERIES [J].
ASKEY, R ;
WAINGER, S .
DUKE MATHEMATICAL JOURNAL, 1966, 33 (01) :223-&
[4]   Remarks on mean convergence (boundedness) of partial sums of trigonometric series [J].
Belov, AS .
MATHEMATICAL NOTES, 2002, 71 (5-6) :739-748
[5]  
Bingham N. H., 1987, Regular Variation
[6]  
BOAS RP, 1965, P LONDON MATH SOC A, V14, P38, DOI DOI 10.1112/PLMS/S3-14A.1.38
[7]  
Chaundy TW, 1916, P LOND MATH SOC, V15, P214
[8]  
Chen CP, 1996, STUD MATH, V118, P245
[9]   Asymptotic behavior of trigonometric series with O-regularly varying quasimonotone coefficients, II [J].
Chen, CP ;
Chen, LK .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 245 (01) :297-301
[10]   Asymptotic behavior of trigonometric series with O-regularly varying quasimonotone coefficients [J].
Chen, CP ;
Chen, L .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 250 (01) :13-26
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