Abstract
Natural metrics in the hyperbolic α-Bloch-, weighted Dirichlet- and Q p -classes are introduced, and these classes are shown to be complete metric spaces with respect to the corresponding metrics. Then Lipschitz continuous and compact composition operators C φ (f) = f ◦ φ acting from the hyperbolic α-Bloch-class to the hyperbolic weighted Dirichlet- or Q p -class are characterized by conditions depending on the symbol φ only.
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