Compact composition operators on Hardy-Orlicz and weighted Bergman-Orlicz spaces on the ball
نویسندگان
چکیده
Using recent characterizations of the compactness of composition operators on HardyOrlicz and Bergman-Orlicz spaces on the ball ([2, 3]), 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, although it is well-known that a map whose range is contained in some nice Korányi approach region induces a compact composition operator on H p (BN) or on A p α (BN), we prove that, for each Korányi region Γ, there exists a map φ : BN → Γ such that, Cφ is not compact on Hψ (BN), when ψ grows fast. Finally, we extend (and simplify the proof of) a result by K. Zhu for classical weighted Bergman spaces, by showing that, under reasonable conditions, a composition operator Cφ is compact on the weighted Bergman-Orlicz space A ψ α (BN), if and only if
منابع مشابه
Carleson Measure Theorems for Large Hardy-orlicz and Bergman-orlicz Spaces
We characterize those measures μ for which the Hardy-Orlicz (resp. weighted Bergman-Orlicz) space HΨ1 (resp. AΨ1 α ) of the unit ball of CN embeds boundedly or compactly into the Orlicz space LΨ2 ( BN ,μ ) (resp. LΨ2 (BN ,μ)), when the defining functions Ψ1 and Ψ2 are growth functions such that L1 ⊂ LΨ j for i, j ∈ {1,2}, and such that Ψ2/Ψ1 is non-decreasing. We apply our result to the charact...
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