Compact composition operators on Bergman-Orlicz spaces
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- by Pascal Lefèvre, Daniel Li, Hervé Queffélec and Luis Rodríguez-Piazza PDF
- Trans. Amer. Math. Soc. 365 (2013), 3943-3970 Request permission
Abstract:
We construct an analytic self-map $\varphi$ of the unit disk and an Orlicz function $\Psi$ for which the composition operator of symbol $\varphi$ is compact on the Hardy-Orlicz space $H^\Psi$, but not on the Bergman-Orlicz space ${\mathfrak B}^\Psi$. 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 $2$.References
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Additional Information
- Pascal Lefèvre
- Affiliation: Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956, Université Lille-Nord-de-France UArtois, F-62 300 Lens, France
- Email: pascal.lefevre@euler.univ-artois.fr
- Daniel Li
- Affiliation: Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956, Université Lille-Nord-de-France UArtois, Faculté des Sciences Jean Perrin, Rue Jean Souvraz, S.P.\kern1mm 18, F-62 300 Lens, France
- MR Author ID: 242499
- Email: daniel.li@euler.univ-artois.fr
- Hervé Queffélec
- Affiliation: Laboratoire Paul Painlevé U.M.R. CNRS 8524, Université Lille-Nord-de-France USTL, F-59655 Villeneuve D’Ascq Cedex, France
- Email: Herve.Queffelec@univ-lille1.fr
- Luis Rodríguez-Piazza
- Affiliation: Facultad de Matemáticas, Departamento de Análisis Matemático & IMUS, Universidad de Sevilla, Apartado de Correos 1160, 41 080 Sevilla, Spain
- MR Author ID: 245308
- Email: piazza@us.es
- Received by editor(s): May 4, 2010
- Published electronically: April 24, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 3943-3970
- MSC (2010): Primary 47B33; Secondary 30J10, 30H10, 30J99, 46E15
- DOI: https://doi.org/10.1090/S0002-9947-2013-05922-3
- MathSciNet review: 3055685