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 ${\mathfrak B}^p = L^2_a (\D)$. In this conference, 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 ${\mathfrak B}^\Psi$. This comes from joint works with P. Lefèvre, H. Queffélec and L. Rodr{\'\i}guez-Piazza.
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• HAL Id : hal-00530387, version 1
• ARXIV : 1010.6207

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Daniel Li. Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces. 2010. ⟨hal-00530387v1⟩

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