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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Composition operators
on weighted Dirichlet spaces

Author: Nina Zorboska
Journal: Proc. Amer. Math. Soc. 126 (1998), 2013-2023
MSC (1991): Primary 47B38; Secondary 30H05
MathSciNet review: 1443862
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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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Nina Zorboska
Affiliation: Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

Keywords: Composition operators, Dirichlet spaces, Carleson measures, angular derivatives.
Received by editor(s): March 13, 1996
Received by editor(s) in revised form: December 10, 1996
Additional Notes: The author was supported in part by an NSERC grant.
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1998 American Mathematical Society