Compact embeddings of model subspaces of the Hardy space

Details Compact embeddings of model subspaces of the Hardy space Compact embeddings of model subspaces of the Hardy space

2007-12-05

arxiv.org/abs/0712.0684v1

Izvestia Mathematics, 73 (2009), 6, 1077-1100 (revised version)

Mathematics

Complex Variables

26 pages

Scientific paper

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

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