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
• DOI: 10.4067/S0716-09172013000200003
• 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.

• Referencias bibliográficas
  • Citas [1] Castillo R., The Nemytskii operator on bounded p-variation in the mean spaces, Matemticas: Enseanza Universitaria Vol XIX, N 1,...
  • [2] Castillo, R., and Trousselot, E., On functions of (p, α)-bounded variation. Real Anal. Exchange, 34, n. 1 , pp. 49-60, (2009).
  • [3] Jordan, C., Sur la Serie de Fourier, C. R. Math. acad. Sci. Paris, 2, pp. 228-230, (1881).
  • [4] Maligranda, L. and Orlicz, W., On some properties of Functions of Generalize Variation, Monatshif fr Mathematik (springe Verlag), 104,...
  • [5] Merentes, N., Functions of bounded (Φ, 2) Variation Annals Univ Sci Budapest, XXXIV, pp. 145-154, (1991).
  • [6] Merentes, N., On Functions of bounded (p, 2)-variation. Collect Math, 43, 2, pp. 115-118, (1992).
  • [7] Merentes, N. y Rivas, S., El Operador de composicin con algn tipo de variacin acotada, IX Escuela de Matematica, AMV, IVIC, (1996).
  • [8] Medved’ev, Y., A generalization of certain Theorem of Riesz, Uspekhi. Mat. Nauk, 6, pp. 115-118, (1953).
  • [9] Mricz, F. and Siddiqi, A. H., A quatified version of the Dirichlet-Jordan test in L1-norm, Rend. Circ. Mat. Palermo, 45, pp. 19-24, (1996).
  • [10] Neves, M. T., Φ-variacin en el sentido de wiener y Riesz, Trabajo de pasanta (asesorado por S. Rivas) UNA Centro local Aragua, rea de...
  • [11] Riesz, F., Untersuchungen ber system intergrierbarer function, Mathematische Annalen, 69, pp. 1449-1497, (1910).
  • [12] Schramm, M., Functions of Φ-Bounded variation and RiemannStieltjes Integration. Trans of the Amer Math. Soc., 287, 1, pp. 46-63, (1985).
  • [13] Waterman, D., On Λ-Bounded Variation, Studia Mathematicae, LVII, pp. 33-45, (1976)