Compact embeddings of model subspaces of the Hardy space

Abstract

We study embeddings of model (star-invariant) subspaces K p Θ of the Hardy space H p , associated with an inner function Θ. We obtain a criterion for the compactness of the embedding of K p Θ into L p (µ) analogous to the Volberg-Treil theorem on bounded embeddings and answer a question posed by Cima and Matheson. The proof is based on Bernstein inequalities for functions in K p Θ . Also we study measures µ such that the embedding operator belongs to a Schatten-von Neumann ideal.