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

DOI:
https://doi.org/10.1090/S0002-9939-98-04206-3

MathSciNet review:
1443167

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-98-04206-3

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