Open Access
2011/2012 BVp-Functions and Change of Variable
N. Merentes, J. L. Sánchez
Real Anal. Exchange 37(1): 177-188 (2011/2012).


In this note we discuss some interconnections between the space \(BV_p[a,b]\) (\(1\leq p\lt\infty\)) of functions of bounded \(p\)-variation (in Wiener's sense) and the space \(Lip_\alpha[a,b]\) (\(0\lt\alpha\leq 1\)) of Hölder continuous functions. In particular, we show that \(f\in BV_p[a,b]\) if and only if \(f=g\circ \tau\), with \(g\in Lip_{1/p}[a,b]\) and \(\tau\) being monotone, and that \(f\in BV_p[a,b] \cap C[a,b]\) if and only if \(f=g\circ \tau\), with \(g\in Lip_{1/p}[a,b]\) and \(\tau\) being a homeomorphism.


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N. Merentes. J. L. Sánchez. "BVp-Functions and Change of Variable." Real Anal. Exchange 37 (1) 177 - 188, 2011/2012.


Published: 2011/2012
First available in Project Euclid: 30 April 2012

MathSciNet: MR3016858

Primary: 26A16 , 26A45
Secondary: 26A48

Keywords: bounded \(p\)-variation , Hölder continuity , homeomorphism, change of variables

Rights: Copyright © 2011 Michigan State University Press

Vol.37 • No. 1 • 2011/2012
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