Almost Everywhere Convergence of Fejer Means of Two-dimensional Triangular Walsh-Fourier Series

被引：11
|
作者：
Gat, Gyoergy [1 ]
机构：
[1] Univ Debrecen, Inst Math, Pf 400, H-4002 Debrecen, Hungary
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2018年 / 24卷 / 05期
关键词：
Fejer means; Triangle Walsh-Paley-Fourier series; a; e; convergence; 42C10; SUMMABILITY; DIVERGENCE;
D O I：
10.1007/s00041-017-9566-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In 1987 Harris proved ( ProcAmMath Soc 101( 4): 637- 643, 1987)- among others- that for each 1 = p < 2 there exists a two- dimensional function f. L p such that its triangular Walsh- Fourier series diverges almost everywhere. In this paper we investigate the Fejer ( or ( C, 1)) means of the triangle two variableWalsh- Fourier series of L1 functions. Namely, we prove the a. e. convergence s n f = 1 n n- 1 k= 0 Sk, n- k f. f ( n.8) for each integrable two- variable function f
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页码：1249 / 1275
页数：27
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