Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Composition operators between Bergman and Hardy spaces

Author: Wayne Smith
Journal: Trans. Amer. Math. Soc. 348 (1996), 2331-2348
MSC (1991): Primary 47B38; Secondary 30D55, 46E15
MathSciNet review: 1357404
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Abstract: We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

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Wayne Smith
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822

Keywords: Bergman spaces, Hardy spaces, composition operators, Nevanlinna counting function
Received by editor(s): February 23, 1995
Article copyright: © Copyright 1996 American Mathematical Society