Composition operators: to the Bloch space to Q_β
Tom 139 / 2000
Studia Mathematica 139 (2000), 245-260
DOI: 10.4064/sm-139-3-245-260
Streszczenie
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.