Approximation by Vilenkin-Fourier sums
type: Item
instance of: scholarly article
title: Approximation by Vilenkin-Fourier sums
zbMATH Open document ID: 0636.42026
DOI: 10.1007/BF01949122
published in: Acta Mathematica Hungarica
publication date: 1986-01-01T00:00:00Z
review text: The author deals with the connection among the Vilenkin-Fourier sums, the modulus of continuity and the Lebesgue-constants with respect to the Vilenkin-system. The author proves five interesting theorems and he remarks that three of them can be also proved in the classical spaces \(C(\ell)\) and \(L^ p(\ell)\) \((\ell \leq p<\infty)\) with the classical modulus of continuity. For notations we refer to the paper. Six theorems are proved. We give the first as an example: 1. For all sequences \(m:=\{m_ k(\geq 2)\}\) and \(f\in L^ p(G_ m)(1<p<\infty)\liminf_{k\to \infty}\| f-S_ kf\|_ p/\omega (f,L^ p,1/k)L_ k=0.\)
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 4036408
zbMATH Keywords: Vilenkin-Fourier sums
zbMATH Keywords: modulus of continuity
zbMATH Keywords: Lebesgue-constants
zbMATH Keywords: Vilenkin-system
author: Sándor Fridli
reviewed by: László Leindler
MaRDI profile type: Publication
cites work: Extensions of Hardy spaces and their use in analysis
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description: scientific article; zbMATH DE number 4036408