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Composition operators on Hardy-Orlicz spaces


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Author: Lefèvre, Pascal
Li, Daniel
Queffélec, Hervé
Rodríguez Piazza, Luis
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2010
Published in: Memoirs of the American Mathematical Society, 207 (974), 1-80.
Document type: Article
Abstract: We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function Ψ grows rapidly: compactness, weak compactness, to be p-summing, order bounded,..., and show how these notions behave according to the growth of Ψ. We introduce an adapted version of Carleson measure. We construct various examples showing that our results are essentially sharp. In the last part, we study the case of Bergman-Orlicz spaces.
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DOI: 10.1090/S0065-9266-10-00580-6

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