\(BV_{p}\)-functions and change of variable (Q418217)

Interconnections between the space \(BV_p[a,b]\) (\(1\leq p <\infty)\) of functions of bounded \(p\)-variation (in Wiener's sense) and the space \(Lip_{\alpha}[a,b]\) (\(0<\alpha\leq 1\)) of Hölder continuous functions are discussed. In particular, it is shown 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.