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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Composition operators that improve integrability on weighted Bergman spaces


Authors: Wayne Smith and Liming Yang
Journal: Proc. Amer. Math. Soc. 126 (1998), 411-420
MSC (1991): Primary 47B38; Secondary 30D55, 46E15
MathSciNet review: 1443167
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Abstract: Composition operators between weighted Bergman spaces with a smaller exponent in the target space are studied. An integrability condition on a generalized Nevanlinna counting function of the inducing map is shown to characterize both compactness and boundedness of such an operator. Composition operators mapping into the Hardy spaces are included by making particular choices for the weights.


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Additional Information

Wayne Smith
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email: wayne@math.hawaii.edu

Liming Yang
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email: yang@math.hawaii.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04206-3
PII: S 0002-9939(98)04206-3
Keywords: Bergman spaces, Hardy spaces, composition operators, Nevanlinna counting function
Received by editor(s): July 24, 1996
Additional Notes: The second author was partially supported by National Science Foundation grant DMS9531917 and a seed-money grant from the University of Hawaii.
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1998 American Mathematical Society