2009/10/28 by Lefèvre, Pascal, Li, Daniel, Queffélec, Hervé +1
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.0910.5368
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 HΨ, but not compact on the Bergman-Orlicz space \mathfrak BΨ. 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.