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arXiv · 0910.5368

Compact composition operators on Bergman-Orlicz spaces

Pascal Lefèvre·Daniel Li·Hervé Queffélec·Luis Rodriguez-Piazza
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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 $H^Ψ$, but not compact on the Bergman-Orlicz space ${\mathfrak B}^Ψ$. 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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Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. 2010-05-31. Compact composition operators on Bergman-Orlicz spaces. https://arxiv.org/abs/0910.5368

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