Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces
We construct an analytic self-map ϕ of the unit disk and an Orlicz function Ψ for which the composition operator of symbol ϕ is compact on the Hardy-Orlicz space HΨ, but not on the Bergman-Orlicz space BΨ. For that, we first prove a Carleson embedding theorem, and then characterize the compactness o...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/44879 |
| Acceso en línea: | http://hdl.handle.net/11441/44879 https://doi.org/10.1007/s13398-011-0027-5 |
| Access Level: | acceso abierto |
| Palabra clave: | Bergman-Orlicz space Carleson function Compactness Composition operator Hardy-Orlicz space Nevanlinna counting function |
| Sumario: | We construct an analytic self-map ϕ of the unit disk and an Orlicz function Ψ for which the composition operator of symbol ϕ is compact on the Hardy-Orlicz space HΨ, but not on the Bergman-Orlicz space BΨ. For that, we first prove a Carleson embedding theorem, and then characterize the compactness of composition operators on Bergman-Orlicz spaces, in terms of Carleson function (of order 2). We show that this Carleson function is equivalent to the Nevanlinna counting function of order 2. |
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