Embeddings of model subspaces of the Hardy space: compactness and Schatten-von Neumann ideals

We study properties of the embedding operators of model subspaces KpΘ (defined by inner functions) in the Hardy space Hp (coinvariant subspaces of the shift operator). We find a criterion for the embedding of KpΘ in Lp(μ) to be compact similar to the Volberg-Treil theorem on bounded embeddings, and give a positive answer to a question of Cima and Matheson. The proof is based on Bernstein-type inequalities for functions in KpΘ. We investigate measures μ such that the embedding operator belongs to some Schatten-von Neumann ideal.