El operador de Nemytskii en espacios de variación acotada generalizados

• Castillo, René Erlín ^[1] ; Rafeiro, Humberto ^[2] ; Trousselot, Eduard ^[3]
  1. [1] Universidad Nacional de Colombia

     Universidad Nacional de Colombia

     Colombia

     
  2. [2] Pontífica Universidad Javeriana

     Pontífica Universidad Javeriana

     Colombia

     
  3. [3] Universidad de Oriente

     Universidad de Oriente

     Venezuela

     

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• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 32, Nº. 1, 2014 (Ejemplar dedicado a: Revista Integración), págs. 71-90
• Idioma: español
• Títulos paralelos:
  • Nemytskii operator on generalized bounded variation space
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

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

  • English

    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.

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