Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 32 No. 1 (2014): Revista Integración, temas de matemáticas
Research and Innovation Articles

Nemytskii operator on generalized bounded variation space

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  • René Erlín Castillo,
  • Humberto Rafeiro,
  • Eduard Trousselot
René Erlín Castillo
Universidad Nacional de Colombia
Humberto Rafeiro
Pontificia Universidad Javeriana
Eduard Trousselot
Universidad de Oriente

Published 2014-05-22

Keywords

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

How to Cite

Castillo, R. E., Rafeiro, H., & Trousselot, E. (2014). Nemytskii operator on generalized bounded variation space. Revista Integración, Temas De matemáticas, 32(1), 71–90. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064

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.

 

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