On summability in \(L^p\)-norm on general Vilenkin groups
type: Item
instance of: scholarly article
title: On summability in \(L^p\)-norm on general Vilenkin groups
zbMATH Open document ID: 0969.42013
author: Muharem Avdispahić
author: Medo Pepić
published in: Taiwanese Journal of Mathematics
publication date: 2001-10-03T00:00:00Z
review text: Let \((\chi_k, k\in \mathbb{N})\) be the Vilenkin system, \(\widehat f(k)\) be the \(k\)th Vilenkin-Fourier coefficient and \[ L_n(\Lambda, f)= \sum^n_{k=0} \lambda_{n,k}\widehat f(k)\chi_k, \] where \(\Lambda= [\lambda_{n,k}]\) and \(\lambda_{n,0}= 1\), \(\lambda_{n,k}= 0\) for all \(k> n\) \((n\in\mathbb{N})\). Sufficient conditions are given such that \(\lim_{n\to\infty} L_n(\Lambda, f)= f\) in \(L^q\) norm \((1\leq q\leq\infty)\). If the Vilenkin system is bounded then this result coincides with an earlier one of Blyumin.
reviewed by: Ferenc Weisz
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 43A55
Mathematics Subject Classification ID: 42B08
zbMATH DE Number: 1512910
zbMATH Keywords: summability in norm
zbMATH Keywords: Vilenkin-Fourier series
zbMATH Keywords: Vilenkin system
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500407233
OpenAlex ID: W1842877459
DOI: 10.11650/TWJM/1500407233
description: scientific article; zbMATH DE number 1512910