Open Access
2008/2009 On Functions of (p,α)-Bounded Variation
René Erlín Castillo, Eduard Trousselot
Real Anal. Exchange 34(1): 49-60 (2008/2009).

Abstract

In this paper we introduce the concept of (p,α)-bounded variation which generalizes the Riesz p-variation. The following result is proved: a function f:[a,b]R is of (p,α)-bounded variation (1<p<) if and only if f is α-absolutely continuous on [a,b] and fαL(p,α)[a,b]. Moreover it is shown that the (p,α)-bounded variation of a function f on [a,b] is given by V(p,α)(f)=fαL(p,α)[a,b]p.

Citation

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René Erlín Castillo. Eduard Trousselot. "On Functions of (p,α)-Bounded Variation." Real Anal. Exchange 34 (1) 49 - 60, 2008/2009.

Information

Published: 2008/2009
First available in Project Euclid: 19 May 2009

MathSciNet: MR2527121

Subjects:
Primary: 26A45 , 26B30
Secondary: 26A16 , 26A24

Keywords: (p,α)-bounded variation , Riesz p-variation

Rights: Copyright © 2008 Michigan State University Press

Vol.34 • No. 1 • 2008/2009
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