On the composition operator in RV [a, b]

Autores: Nelson Merentes
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 46, Fasc. 3, 1995 (Ejemplar dedicado a: Professor Paul Dubreil (In memoriam )), págs. 231-238
Idioma: inglés
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Resumen
- We shall denote by $F$ the composition operator generated by a given function $f : \mathbb{R}\rightarrow\mathbb{R}$, acting on the space of functions of bounded Riesz $\Phi$-variation. In this paper we prove that the composition operator $F$ maps the space $RV_\Phi[a, b]$ into itself if and only if $f$ satisfies a local Lipschitz condition on $\mathbb{R}$.