Composition operators: $N_α$ to the Bloch space to $Q_β$

Tom 139 / 2000

Jie Xiao Studia Mathematica 139 (2000), 245-260 DOI: 10.4064/sm-139-3-245-260


Let $N_α$,B and Q_β be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and $Q_β$ are Möbius invariant, but $N_α$ is not. We characterize, in function-theoretic terms, when the composition operator $C_ϕ f=f◦ϕ$ induced by an analytic self-map ϕ of the unit disk defines an operator $C_ϕ:N_α→B$, $B→Q_β$, $N_α→Q_β$ which is bounded resp. compact.


  • Jie Xiao

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