The Nemytskii operator on bounded φ-variation in the mean spaces

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

     Universidad Nacional de Colombia

     Colombia

     
  2. [2] Universidad Central de Venezuela

     Universidad Central de Venezuela

     Venezuela

     
  3. [3] Universidad de Oriente

     Universidad de Oriente

     Venezuela

     

  Mostrar afiliaciones +
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 32, Nº. 2, 2013, págs. 119-142
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We introduce the notion of bounded Φ-variation in the sense of L^-norm. We obtain a Riesz type result for functions of bounded Φ-variation in the mean. We also show that if the Nemytskii operator act on the bounded Φ-variation in the mean spaces into itself and satisfy some Lipschitz condition there exist two functions g and h belonging to the bounded Φ-variation in the mean space such that f (t,y) = g(t)y + h(t),t G [0, 2π],y G.