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

Abstract : It is known, from results of B. MacCluer and J. Shapiro (1986), that every composition operator which is compact on the Hardy space $H^p$, $1 \leq p < \infty$, is also compact on the Bergman space ${\mathfrak B}^p = L^p_a (\D)$. In this survey, after having described the above known results, we consider Hardy-Orlicz $H^\Psi$ and Bergman-Orlicz ${\mathfrak B}^\Psi$ spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on $H^\Psi$ but not on ${\mathfrak B}^\Psi$.
Keywords :
Type de document :
Pré-publication, Document de travail
2011

Littérature citée [16 références]

https://hal-univ-artois.archives-ouvertes.fr/hal-00530387
Contributeur : Daniel Li <>
Soumis le : lundi 21 mars 2011 - 10:43:40
Dernière modification le : lundi 21 mars 2011 - 15:16:18
Document(s) archivé(s) le : mercredi 22 juin 2011 - 09:53:28

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• HAL Id : hal-00530387, version 2
• ARXIV : 1010.6207

### Citation

Daniel Li. Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces. 2011. 〈hal-00530387v2〉

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