On the modulus of continuity with respect to functions defined on Vilenkin groups
type: Item
instance of: scholarly article
title: On the modulus of continuity with respect to functions defined on Vilenkin groups
zbMATH Open document ID: 0569.43006
DOI: 10.1007/BF01957037
published in: Acta Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: We generalize a theorem of \textit{A. I. Rubinshtejn} [Mat. Zametki 23, 379- 388 (1978; Zbl 0405.43006)]. By the usual definition the modulus of continuity of a function defined on a Vilenkin group, \(G_ m\), can be represented by a sequence of real numbers. Rubinshtejn characterized the sequences which turn to be the modulus of continuity of a function in \(C(G_ m)\), \(L^ 1(G_ m)\), \(L^ 2(G_ m)\). Now we prove his conjecture, namely the theorem is true for \(L^ p(G_ m)\) \((1\leq p<\infty)\) too.
Mathematics Subject Classification ID: 43A77
Mathematics Subject Classification ID: 26A15
zbMATH DE Number: 3909051
zbMATH Keywords: modulus of continuity
zbMATH Keywords: Vilenkin group
author: Sándor Fridli
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01957037
OpenAlex ID: W2025073237
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description: scientific article; zbMATH DE number 3909051