2011/01/19 by Charpentier, Stéphane
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1101.3677
Using recent characterizations of the compactness of composition operators on Hardy-Orlicz and Bergman-Orlicz spaces on the ball, we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H∞. Then, we prove that, for each Koranyi region Γ, there exists a map ϕtaking the ball into Γsuch that, Cϕ is not compact on Hψ(\mathbbBN), when ψgrows fast. Finally, we give another characterization of the compactness of composition operator on weighted Bergman-Orlicz spaces in terms of an Orlicz "Angular derivative"-type condition. This extends (and simplify the proof of) a result by K. Zhu for the classical Bergman case. Moreover, we deduce that the compactness of composition operators on weighted Bergman-Orlicz spaces does not depend on the weight anymore, when the Orlicz function grows fast.