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Geometric models for composition operators between Bergman and Hardy spaces. (English) Zbl 0862.47016
Laine, Ilpo (ed.) et al., 16th Rolf Nevanlinna colloquium. Proceedings of the international conference held in Joensuu, Finland, August 1–5, 1995. Berlin: de Gruyter. 223-229 (1996).
Summary: We study composition operators induced by univalent selfmaps of the unit disk. In this case, the principal eigenfunction of the operator provides a simple geometric model for the operator’s inducing map. This model is used to give a geometric characterization of when the composition operator is bounded or compact from one Bergman or Hardy space to another such space.
##### MSC:
 47B38 Operators on function spaces (general) 46E15 Banach spaces of continuous, differentiable or analytic functions 46J15 Banach algebras of differentiable or analytic functions, ${H}^{p}$-spaces