Bounded holomorphic functions on bounded symmetric domains
Authors:
Joel M. Cohen and Flavia Colonna
Journal:
Trans. Amer. Math. Soc. 343 (1994), 135156
MSC:
Primary 32A37; Secondary 32M15, 46E15
MathSciNet review:
1176085
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Abstract: Let D be a bounded homogeneous domain in , and let denote the open unit disk. If and is holomorphic, then is defined as the maximum ratio , where x is a nonzero vector in and is the Bergman metric on D. The number represents the maximum dilation of f at z. The set consisting of all for and holomorphic, is known to be bounded. We let , be its least upper bound. In this work we calculate for all bounded symmetric domains having no exceptional factors and give indication on how to handle the general case. In addition we describe the extremal functions (that is, the holomorphic functions f for which ) when D contains as a factor, and show that the class of extremal functions is very large when is not a factor of D.
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 M. Ise, Bounded symmetric domains of exceptional type, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), 75105. MR 0419860 (54:7878)
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 S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, Marcel Dekker, New York, 1970. MR 0277770 (43:3503)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199411760856
PII:
S 00029947(1994)11760856
Keywords:
Bloch,
bounded symmetric domains,
Lipschitz
Article copyright:
© Copyright 1994
American Mathematical Society
