Artículo
Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk
Autor/es | Li, Daniel
Queffélec, Hervé Rodríguez Piazza, Luis |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2013-08 |
Fecha de depósito | 2016-09-29 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | Ministerio de Ciencia e Innovación (MICIN). España |
Identificador del proyecto | MTM 2009-08934 |
Cita | Li, D. y Queffélec, H. (2013). Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk. Complex Analysis and Operator Theory, 7 (4), 1371-1387. |
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