Global integral criteria for composition operators |
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| Authors: | K-J Wirths |
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| Institution: | a Institut für Analysis, TU Braunschweig, D-38106 Braunschweig, Germany
b Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, H3G 1M8 Montreal, PQ, Canada |
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| Abstract: | Let Dα denote the Dirichlet-type space of functions analytic on the unit disk U and Qα the conformal invariant version of this space. Any analytic self-map φ of U induces a composition operator Cφ acting on Dα, respectively, Qα by Cφf=f°φ, where f∈Dα, respectively, f∈Qα. The aim of this paper is to characterize boundedness and compactness of such operators in terms of global area integrals of φ. |
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| Keywords: | Global area integrals Composition operators Boundedness Compactness Dirichlet-type spaces Q-spaces |
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