Title :

Compact composition operators on Bergman-Orlicz spaces

Author(s) :

Lefèvre, Pascal [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Li, Daniel [Auteur correspondant]
Laboratoire de Mathématiques de Lens [LML]
Queffélec, Hervé [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rodriguez-Piazza, Luis [Auteur]

English keyword(s) :

Bergman-Orlicz space
Carleson function
Compactness
Composition operator
Hardy-Orlicz space
Nevanlinna counting function

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

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 ...
Show more >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 $2$.Show less >

Language :

Anglais

Comment :

32 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T12:52:07Z