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Compact composition operators on Bergman-Orlicz spaces

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Pascal Lefèvre
Daniel Li
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Hervé Queffélec
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  • PersonId : 859618
Luis Rodriguez-Piazza
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  • PersonId : 859619

Abstract

We construct an analytic self-map $\phi$ of the unit disk and an Orlicz function $\Psi$ for which the composition operator of symbol $\phi$ is compact on the Hardy-Orlicz space $H^\Psi$, but not compact 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 $2$.
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Dates and versions

hal-00426831 , version 1 (28-10-2009)
hal-00426831 , version 2 (30-03-2010)

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Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Compact composition operators on Bergman-Orlicz spaces. 2010. ⟨hal-00426831v2⟩
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