APPROXIMATION BY Θ-MEANS OF WALSH-FOURIER SERIES

被引：32

作者：

Blahota, I. ^{[1
]}

Nagy, K. ^{[1
]}

机构：

[1] Univ Nyiregyhaza, Inst Math & Comp Sci, POB 166, H-4400 Nyiregyhaza, Hungary

来源：

ANALYSIS MATHEMATICA | 2018年 / 44卷 / 01期

关键词：

Walsh group; Walsh system; Walsh-Fourier series; Norlund mean; weighted mean; approximation; modulus of continuity; Lipschitz function; Theta-mean; NORLUND MEANS; HARDY-SPACES; COEFFICIENTS; SUMMABILITY;

D O I：

10.1007/s10476-018-0106-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the behaviour of the Theta-means of Walsh series of a function in L-p (1 <= p <= infinity). We investigate the rate of the approximation by this means, in particular, in Lip(alpha, p), where alpha > 0 and 1 <= p <= 8. In case p = infinity by L-p we mean C, the class of the continuous functions. Our main theorems give a common generalization of two results of Moricz and Siddiqi on Norlund means [11] and Moricz and Rhoades on weighted means [9].

引用

页码：57 / 71

页数：15

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