Composition operators on weighted Dirichlet spaces

Zorboska, Nina

doi:10.1090/S0002-9939-98-04266-X

Composition operators on weighted Dirichlet spaces
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Proc. Amer. Math. Soc. 126 (1998), 2013-2023 Request permission

Abstract:

We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. We also present several examples and counter-examples that point out the borderlines of the result and its connections to other themes.

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