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| Detailed view | Preprint, Working Paper, ... |
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| Available versions: | v1 (2010-10-29) | v2 (2011-03-21) |
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| Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces |
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| Daniel Li1 |
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| It is known, from results of B. MacCluer and J. Shapiro (1986), that every composition operator which is compact on the Hardy space $H^p$, $1 \leq p < \infty$, is also compact on the Bergman space ${\mathfrak B}^p = L^p_a (\D)$. In this survey, after having described the above known results, we consider Hardy-Orlicz $H^\Psi$ and Bergman-Orlicz ${\mathfrak B}^\Psi$ spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on $H^\Psi$ but not on ${\mathfrak B}^\Psi$. |
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| 1: | LML - Laboratoire de Mathématiques de Lens |
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| Bergman spaces – Bergman-Orlicz spaces – Blaschke product – Carleson function – Carleson measure – compactness – composition operator – Hardy spaces – Hardy-Orlicz spaces – Nevanlinna counting function |
| hal-00530387, version 2 | |
| http://hal-univ-artois.archives-ouvertes.fr/hal-00530387 | |
| oai:hal-univ-artois.archives-ouvertes.fr:hal-00530387 | |
| From: Daniel Li | |
| Submitted on: Monday, 21 March 2011 10:43:40 | |
| Updated on: Monday, 21 March 2011 15:16:18 | |
