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A sharp Schwarz inequality on the boundary
Author(s):
Robert
Osserman
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3513-3517.
MSC (2000):
Primary 30C80
Posted:
May 18, 2000
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Abstract:
A number of classical results reflect the fact that if a holomorphic function maps the unit disk into itself, taking the origin into the origin, and if some boundary point  maps to the boundary, then the map is a magnification at  . We prove a sharp quantitative version of this result which also sharpens a classical result of Loewner.
References:
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Additional Information:
Robert
Osserman
Affiliation:
MSRI, 1000 Centennial Drive, Berkeley, California 94720-5070
Email:
osserman@msri.org
DOI:
10.1090/S0002-9939-00-05463-0
PII:
S 0002-9939(00)05463-0
Keywords:
Schwarz Lemma
Received by editor(s):
June 15, 1998
Received by editor(s) in revised form:
January 26, 1999
Posted:
May 18, 2000
Additional Notes:
The author's research at MSRI is supported in part by NSF grant DMS-9701755.
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
2000,
American Mathematical Society
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