A remark on the divergence of strong power means of Walsh-Fourier series

被引：1
|
作者：
Gat, G. [1 ]
Goginava, U. [2 ]
Karagulyan, G. [3 ]
机构：
[1] Coll Nyiregyhaza, Inst Math & Comp Sci, Nyiregyhaza, Hungary
[2] Tbilisi State Univ, Dept Math, Fac Exact & Nat Sci, GE-380086 Tbilisi, Georgia
[3] Armenian Natl Acad Sci, Inst Math, Yerevan, Armenia
来源：
MATHEMATICAL NOTES | 2014年 / 96卷 / 5-6期
关键词：
Walsh series; strong summability; everywhere divergent Walsh-Fourier series; STRONG APPROXIMATION; STRONG SUMMABILITY; BMO;
D O I：
10.1134/S0001434614110261
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
F. Schipp in 1969 proved the almost everywhere p-strong summability of Walsh-Fourier series and showed that if lambda(n)-> a, then there exists a function f a L (1)[0, 1) for which the Walsh partial sums S (k) (x, f) satisfy the divergence condition lim sup(n ->infinity) 1/n (k=1)Sigma(n) vertical bar S-k (x, f)vertical bar lambda((k)) = infinity almost everywhere on [0, 1). In the present paper, we show that this condition holds everywhere.
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页码：897 / 903
页数：7
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