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Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

 

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Opened Access Compact composition operators on Hardy-Orlicz and Bergman-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: 2011-09
Published in: Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales. Serie A: Matematicas, 105 (2), 247-260.
Document type: Article
Abstract: 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.
Cite: Lefèvre, P., Li, D., Queffélec, H. y Rodríguez Piazza, L. (2011). Compact composition operators on Bergman-Orlicz spaces. Revista de la Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas, 105 (2), 247-260.
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URI: http://hdl.handle.net/11441/44879

DOI: 10.1007/s13398-011-0027-5

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