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Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk

 

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Opened Access Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk
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Author: Li, Daniel
Queffélec, Hervé
Rodríguez Piazza, Luis
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2013-08
Published in: Complex Analysis and Operator Theory, 7 (4), 1371-1387.
Document type: Article
Abstract: 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.
Cite: 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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URI: http://hdl.handle.net/11441/46358

DOI: 10.1007/s11785-012-0244-8

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