Some revisited results about composition operators on Hardy spaces

  • Pascal Lefèvre

    Université d'Artois, Lens, France
  • Daniel Li

    Université d'Artois, Lens, France
  • Hervé Queffélec

    Université Lille I, Villeneuve d'Ascq, France
  • Luis Rodríguez Piazza

    Universidad de Sevilla, Spain


On the one hand, we generalize some results known for composition operators on Hardy spaces to the case of Hardy–Orlicz spaces HΨH^\Psi: construction of a “slow” Blaschke product giving a non-compact composition operator on HΨH^\Psi and yet “nowhere differentiable”; construction of a surjective symbol whose associated composition operator is compact on~HΨH^\Psi and is, moreover, in all Schatten classes Sp(H2)S_p (H^2), p>0p > 0. On the other hand, we revisit the classical case of composition operators on H2H^2, giving first a new, and simpler, characterization of composition operators with closed range, and then showing directly the equivalence of the two characterizations of membership in Schatten classes of Luecking, and Luecking–Zhu.

Cite this article

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodríguez Piazza, Some revisited results about composition operators on Hardy spaces. Rev. Mat. Iberoam. 28 (2012), no. 1, pp. 57–76

DOI 10.4171/RMI/666