On a Problem of Hardy for Walsh-Fourier Series

被引：0
|
作者：
Bochkarev, S. V. [1 ]
机构：
[1] Russian Acad Sci, VA Steklov Math Inst, Moscow 119333, Russia
来源：
DOKLADY MATHEMATICS | 2010年 / 81卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
CONVERGENCE;
D O I：
10.1134/S1064562410030142
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A tight bound (on a logarithmic scale) for the order of growth almost everywhere of partial sums of Walsh- Fourier series has been reported. The currently best lower bound was derived by Konyagin and differs from by the root of a logarithm. The proof of Theorem 1 makes use of an important quadratic function generalizing the Paley function. The result cannot be substantially refined any more and, in a sense, is final.
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页码：390 / 391
页数：2
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