Functions of bounded \(\kappa \varphi\)-variation in the sense of Riesz-Korenblum
type: Item
instance of: scholarly article
title: Functions of bounded \(\kappa \varphi\)-variation in the sense of Riesz-Korenblum
zbMATH Open document ID: 1275.46015
DOI: 10.1155/2013/718507
author: Mariela Castillo
author: Sergio Rivas
author: María Sanoja
author: Iván Zea
published in: Journal of Function Spaces and Applications
publication date: 2013-05-29T00:00:00Z
review text: Summary: We present the space of functions of bounded \(\kappa \varphi\)-variation in the sense of Riesz-Korenblum, denoted by \(\kappa BV_{\varphi}[a, b]\), which is a combination of the notions of bounded \(\varphi\)-variation in the sense of Riesz and bounded \(\kappa\)-variation in the sense of Korenblum. Moreover, we prove that the space generated by this class of functions is a Banach space with a given norm and we prove that a uniformly bounded composition operator satisfies Matkowski's weak condition.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 26A45
zbMATH DE Number: 6167915
zbMATH Keywords: functions of bounded \(\kappa \varphi\)-variation
Wikidata QID: Q59012554
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/718507
OpenAlex ID: W2089743004
cites work: On BV-solutions of some nonlinear integral equations
cites work: Uniformly continuous composition operators in the space of bounded \(\varphi \)-variation functions
cites work: On the Hammerstein-Volterra equation in the space of the absolutely continuous functions
cites work: Q5822683
cites work: An extension of the Nevanlinna theory
cites work: The decomposition of functions of bounded ϰ-variation into differences of ϰ-decreasing functions
cites work: Q4723988
cites work: Q3171818
cites work: Functions of Φ-Bounded Variation and Riemann-Stieltjes Integration
cites work: Uniformly bounded composition operators in the Banach space of bounded \((p, k)\)-variation in the sense of Riesz-Popoviciu
cites work: Uniformly bounded composition operators in the Banach space of absolutely continuous functions
cites work: Uniformly continuous composition operators in the space of bounded \(\Phi \)-variation functions in the Schramm sense
cites work: Uniformly bounded composition operators on a Banach space of bounded Wiener-Young variation functions
cites work: Q4013134
cites work: On characterization of the Lipschitzian composition operator between spaces of functions of bounded $p$-variation
cites work: Q3018973
cites work: Uniformly bounded composition operators between general Lipschitz function normed spaces
cites work: Q5765474
description: scientific article; zbMATH DE number 6167915