On the Composition Operator in AC[a,b]

• Autores: Nelson Merentes
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 42, Fasc. 3, 1991, págs. 237-243
• Idioma: inglés
• Títulos paralelos:
  • Sobre el operador de composición en AC[a,b]
• Enlaces
  • Texto completo
• Resumen

  • Denote by F the composition operator generated by a given function f: R --> R, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.

• Referencias bibliográficas
  • J. Ciemnoczolowski and W. Orlicz, Composing functions of bounded $\phi$-variation, Proc. Amer. Math. Soc. 96, 3 (1986), 431–436.
  • M. Josephy, Composing functions of bounded variation, Proc. Amer. Math. Soc. 83 (1981), 354–356.
  • H. Kestelman, Modern theories of integration, Oxford, 1937.
  • N. Merentes, Composing functions of bounded $p$-variation, Ann. Pol. Math. (submitted).
  • Ch. J. De La Vallée Poussin, Sur l’integrale de Lebesgue, Trans. Amer. Math. Soc. 16 (1915), 435–501.
  • E. Varberg Dale, On absolutely continuous functions, Amer. Math. Monthly 72 (1965), 831–941.