On functions of \((p, \alpha)\)-bounded variation
type: Item
instance of: scholarly article
title: On functions of \((p, \alpha)\)-bounded variation
zbMATH Open document ID: 1179.26032
author: René Erlín Castillo
author: Eduard Trousselot
published in: Real Analysis Exchange
publication date: 2009-07-14T00:00:00Z
review text: The concept of bounded \(p\)-variation introduced by Riesz in the framework of real-valued functions defined on \([a,b]\) is generalized. The new concept is called \((p,\alpha)\)-bounded variation and the related space is denoted by \(BV_{(p,\alpha)}[a,b]\). The following result is established: A function \(f:[a,b]\rightarrow{\mathbb R}\) is of \((p,\alpha)\)-bounded variation (\(1<p<\infty\)) if and only if \(f\) is \(\alpha\)-absolutely continuous on \([a,b]\) and \(f'_\alpha\in L_{(p,\alpha)}[a,b]\).
reviewed by: Teodora-Liliana Rădulescu
Mathematics Subject Classification ID: 26A45
Mathematics Subject Classification ID: 26A16
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 26B30
zbMATH DE Number: 5578213
zbMATH Keywords: Riesz \(p\)-variation
zbMATH Keywords: \((p,\alpha)\)-bounded variation
MaRDI profile type: Publication
full work available at URL: realanalexch.34.1.0049
OpenAlex ID: W1530621034
DOI: 10.14321/REALANALEXCH.34.1.0049
description: scientific article; zbMATH DE number 5578213