Compact embeddings of model subspaces of the Hardy space

Abstract

We study embeddings of model (star-invariant) subspaces $K_{\Theta }^p$ of the Hardy space $H^p$, associated with an inner function $\Theta$. We obtain a criterion for the compactness of the embedding of $K_{\Theta }^p$ into $L^p(\mu )$ 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 $K_{\Theta }^p$. Also we study measures $\mu$ such that the embedding operator belongs to a Schatten--von Neumann ideal.

26 pages

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