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

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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.
Słowa kluczowe
  • Institute of Analysis, TU-Braunschweig PK 14(Forum) D-38106 Braunschweig, Germany
  • School of Mathematical Sciences, Peking University, Beijing 100871, China
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