Resumen de Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

D. Li

• It is known, from results of MacCluer and Shapiro (Canad. J. Math. 38(4):878-906, 1986), that every composition operator which is compact on the Hardy space Hp, 1 ≤ p < ∞, is also compact on the Bergman space Bp = Lpa. In this survey, after having described the above known results, we consider Hardy-Orlicz HΨ and Bergman-Orlicz BΨ spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on HΨ but not on BΨ. © 2011 Springer-Verlag.