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Compactness of composition operators on BMOA
Author(s):
Wayne
Smith
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2715-2725.
MSC (1991):
Primary 47B38;
Secondary 30D50
Posted:
April 15, 1999
MathSciNet review:
1600145
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Abstract:
A function theoretic characterization is given of when a composition operator is compact on BMOA, the space of analytic functions on the unit disk having radial limits that are of bounded mean oscillation on the unit circle. When the symbol of the composition operator is univalent, compactness on BMOA is shown to be equivalent to compactness on the Bloch space, and a characterization in terms of the geometry of the image of the disk under the symbol of the operator results.
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Additional Information:
Wayne
Smith
Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email:
wayne@math.hawaii.edu
DOI:
10.1090/S0002-9939-99-04856-X
PII:
S 0002-9939(99)04856-X
Keywords:
Bounded mean oscillation,
compact composition operators
Received by editor(s):
September 22, 1997
Received by editor(s) in revised form:
November 25, 1997
Posted:
April 15, 1999
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
1999,
American Mathematical Society
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