Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk
We prove that, for every α>−1, the pull-back measure φ(Aα) of the measure dAα(z)=(α+1)(1−|z|2)αdA(z), where A is the normalized area measure on the unit disk D, by every analytic self-map φ:D→D is not only an (α+2)-Carleson measure, but that the measure of the Carleson windows of size εhεh is con...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/46358 |
| Acceso en línea: | http://hdl.handle.net/11441/46358 https://doi.org/10.1007/s11785-012-0244-8 |
| Access Level: | acceso abierto |
| Palabra clave: | Calderón-Zygmund decomposition Carleson measure Weighted Bergman space |
| Sumario: | We prove that, for every α>−1, the pull-back measure φ(Aα) of the measure dAα(z)=(α+1)(1−|z|2)αdA(z), where A is the normalized area measure on the unit disk D, by every analytic self-map φ:D→D is not only an (α+2)-Carleson measure, but that the measure of the Carleson windows of size εhεh is controlled by εα+2 times the measure of the corresponding window of size h. This means that the property of being an (α+2)-Carleson measure is true at all infinitesimal scales. We give an application by characterizing the compactness of composition operators on weighted Bergman-Orlicz spaces. |
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