APPROXIMATION BY NORLUND MEANS OF WALSH-FOURIER SERIES

被引:55
作者
MORICZ, F [1 ]
SIDDIQI, AH [1 ]
机构
[1] ALIGARH MUSLIM UNIV,DEPT MATH,ALIGARH 202002,UTTAR PRADESH,INDIA
关键词
D O I
10.1016/0021-9045(92)90067-X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the rate of approximation by Nörlund means for Walsh-Fourier series of a function in Lp and, in particular, in Lip(α, p) over the unit interval [0, 1), where α > 0 and 1 ≤ p ≤ ∞. In case p = ∞, by Lp we mean CW, the collection of the uniformly W-continuous functions over [0, 1). As special cases, we obtain the earlier results by Yano, Jastrebova, and Skvorcov on the rate of approximation by Cesàro means. Our basic observation is that the Nörlund kernel is quasi-positive, under fairly general assumptions. This is a consequence of a Sidon type inequality. At the end, we raise two problems. © 1992.
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页码:375 / 389
页数:15
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