Embeddings of model subspaces of the Hardy space: compactness and Schatten-von Neumann ideals
Abstract
We study properties of the embedding operators of model subspaces K^p_{\Theta} (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^p_{\Theta} in L^p(\mu) 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 K^p_{\Theta}. We investigate measures \mu such that the embedding operator belongs to some Schatten-von Neumann ideal.
- Publication:
-
Izvestiya: Mathematics
- Pub Date:
- December 2009
- DOI:
- 10.1070/IM2009v073n06ABEH002473
- arXiv:
- arXiv:0712.0684
- Bibcode:
- 2009IzMat..73.1077B
- Keywords:
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- Mathematics - Complex Variables;
- Mathematics - Functional Analysis;
- 30D50;
- 30D55;
- 46E15;
- 46E22
- E-Print:
- 26 pages