Nemytskii operator on generalized bounded variation space

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 f (t, y) = g(t)y + h(t) for all t ∈ [a, b], y ∈ R. 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.

Keywords

• Riesz p-variation
• (φ, α)-bounded variation