Bounded holomorphic functions on bounded symmetric domains

Authors:
Joel M. Cohen and Flavia Colonna

Journal:
Trans. Amer. Math. Soc. **343** (1994), 135-156

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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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1994-1176085-6

Keywords:
Bloch,
bounded symmetric domains,
Lipschitz

Article copyright:
© Copyright 1994
American Mathematical Society