Nemytskii operator on generalized bounded
variation space

RENÉ ERLÍN CASTILLO^a,*, HUMBERTO RAFEIRO^b,
EDUARD TROUSSELOT^c

^a Universidad Nacional de Colombia, Departamento de Matemáticas, Bogotá, Colombia.
^b Pontificia Universidad Javeriana, Departamento de Matemáticas, Bogotá, Colombia.
^c Universidad de Oriente, Departamento de Matemáticas, 6101 Cumaná, Edo. Sucre, Venezuela.

Abstract. In this paper we show that if the Nemytskii operator maps the (φ, α)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the (φ, α)-bounded variation space such that .

Keywords: Riesz p-variation, (φ, α)-bounded variation.
MSC2010: 26A45, 26B30, 26A16, 26A24.

El Operador de Nemytskii en espacios de variación
acotada generalizados

Resumen. En este artículo demostramos que si el operador de Nemytskii lleva el espacio de variación (φ, α)-acotada en sí mismo, y satisface cierta condición de Lipschitz, entonces existen dos funciones g y h perteneciendo al espacio de variación (φ, α)-acotada tal que .

Palabras claves: p-variación de Riesz, variación (φ, α)-acotada.

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*Corresponding author: E-mail: recastillo@unal.edu.co.
Received: 09 November 2013, Accepted: 17 March 2014.
To cite this article: R. E. Castillo, H. Rafeiro, E. Trousselot, Nemytskii operator on generalized bounded
variation space, Rev. Integr. Temas Mat. 32 (2014), no. 1, 71–90.