Sequences of composition operators in spaces of functions of bounded \(\Phi\)-variation
type: Item
instance of: scholarly article
title: Sequences of composition operators in spaces of functions of bounded \(\Phi\)-variation
zbMATH Open document ID: 1194.47025
DOI: 10.1134/S0001434609030031
author: O. E. Galkin
published in: Mathematical Notes
publication date: 2009-11-10T00:00:00Z
review text: The spaces of functions of bounded variation were studied from diverse viewpoints. Here, the authors study conditions on a sequence of functions \(h_n : \langle c,d\rangle \to \langle a,b\rangle\) \((h_n : \mathbb R \to \mathbb R)\), \(n = 1, 2, \dots,\) under which the sequences of operators of right composition \(f\to f\circ h_n\) (of operators of left composition \(f\to h_n \circ f\), respectively) on the space \( BV_{\Phi} \langle a,b\rangle \) is pointwise bounded with respect to \({\Psi}\)-variation (i.e, for any function \(f\) in the class \( BV_{\Phi} \langle a,b\rangle \), the sequence of \({\Psi}\)-variations \(\{V_{\Psi} (\langle c,d \rangle : f\circ h_n)\}_{n= 1}^{\infty }\), \(\{V_{\Psi}(\langle a,b \rangle : h_n \circ f )\}_{n = 1}^{\infty }\) is bounded. The author gives a brief history of the problem.
reviewed by: V. Lokesha
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 26A45
zbMATH DE Number: 5628161
zbMATH Keywords: composition operator
zbMATH Keywords: \(\varphi\)-function
zbMATH Keywords: \(\Phi\)-variation
zbMATH Keywords: modulus of continuity
zbMATH Keywords: Lipschitz function
zbMATH Keywords: Holder property
MaRDI profile type: Publication
cites work: On generalized variations (I)
cites work: On generalized variations (II)
cites work: Composing Functions of Bounded Variation
cites work: Inequalities Connected with Bounded p th Power Variation in the Wiener Sense and with Integrated Lipschitz Conditions
cites work: Mappings of bounded \(\Phi\)-variation with arbitrary function \(\Phi\)
cites work: Composing Functions of Bounded ϕ-Variation
full work available at URL: s0001434609030031
OpenAlex ID: W2007014894
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description: scientific article; zbMATH DE number 5628161