Compact Composition Operators on Model Spaces with Univalent Symbols

Abstract

We give a sufficient condition and a necessary condition for the compactness of the composition operators on model spaces C_ϕ : K_θ → H², where ϕ is univalent. This is a generalization to a result of Shapiro for the composition operator C_ϕ : H² → H², [11].

Key words and phrases. Composition operator, Hardy spaces, model spaces.

1991 Mathematics Subject Classification. 47B33, 47A15