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

We study properties of the embedding operators of model sub-spcaes K(Theta)(p) (defined by inner functions) in the Hardy space H(p) (coinvariant subspaces of the shift operator). We find a criterion for the embedding of K(Theta)(p) in L(p)(mu) to be compact similar to the Volbert 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 K(Theta)(p). We investigate measures mu such that the embedding operator belongs to some Schatten von Neumann ideal.