Trace ideal criteria for embeddings and composition operators on model spaces
| Autor: | Aleman, A., Lyubarskii, Yu., Malinnikova, E., Perfekt, K. -M. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | J. Funct. Anal. 270 (2016), no. 3, 861-883 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jfa.2015.11.006 |
| Popis: | Let $K_\theta$ be a model space generated by an inner function $\theta$. We study the Schatten class membership of embeddings $I : K_\theta \to L^2(\mu)$, $\mu$ a positive measure, and of composition operators $C_\phi:K_\theta\to H^2(\mathbb D)$ with a holomprphic function $\phi:\mathbb D\rightarrow \mathbb D$. In the case of one-component inner functions $\theta$ we show that the problem can be reduced to the study of natural extensions of $I$ and $C_\phi$ to the Hardy-Smirnov space $E^2(D)$ in some domain $D\supset \mathbb D$. In particular, we obtain a characterization of Schatten membership of $C_\phi$ in terms of Nevanlinna counting function. By example this characterization does not hold true for general $\phi$. Comment: 20 pages |
| Databáze: | arXiv |
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