Bloch constants of bounded symmetric domains

Author:
Genkai Zhang

Journal:
Trans. Amer. Math. Soc. **349** (1997), 2941-2949

MSC (1991):
Primary 32H02, 32M15

DOI:
https://doi.org/10.1090/S0002-9947-97-01518-3

MathSciNet review:
1329540

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let and be two irreducible bounded symmetric domains in the complex spaces and respectively. Let be the Euclidean metric on and the Bergman metric on . The Bloch constant is defined to be the supremum of , taken over all the holomorphic functions and , and nonzero vectors . We find the constants for all the irreducible bounded symmetric domains and . As a special case we answer an open question of Cohen and Colonna.

**[CC]**J. M. Cohen and F. Colonna,*Bounded holomorphic functions on bounded symmetric domains*, Trans. Amer. Math. Soc.**343**(1994), 135-156. MR**94g:32007****[He]**S. Helgason,*Differential geometry, Lie groups, and symmetric spaces*, Academic Press, London, 1978. MR**80k:53081****[Hu]**L. K. Hua,*Harmonic analysis of functions of several complex variables in the classical domains*, Amer. Math. Soc., Providence, Rhode Island, 1963. MR**30:2162****[L1]**O. Loos,*Bounded Symmetric Domains and Jordan Pairs*, University of California, Irvine, 1977.**[L2]**O. Loos,*Jordan Pairs*, Lecture Notes in Mathematics, No. 460, Springer, 1975. MR**56:3071****[R]**W. Rudin,*Function Theory in the Unit Ball of*, Springer-Verlag, 1980. MR**82i:32002****[Sa]**I. Satake,*Algebraic structures of symmetric domains*, Iwanami Shoten and Priceton Univ. Press, Tokyo and Princeton, NJ, 1980. MR**82i:32003****[Up]**H. Upmeier,*Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics*, Regional Conference Series in Mathematics No.67, Amer. Math. Soc., 1987. MR**80h:17032****[W]**J. Wolf,*Fine structure of hermitian symmetric spaces*, Symmetric Spaces, Marcel Dekker, New York, 1972, pp. 271-357. MR**53:8516****[Y]**Z. Yan,*Extremal holomorphic mappings between a bounded symmetric domain and the unit ball*, preprint, Berkeley, 1993.

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (1991):
32H02,
32M15

Retrieve articles in all journals with MSC (1991): 32H02, 32M15

Additional Information

**Genkai Zhang**

Affiliation:
School of Mathematics, University of New South Wales, Kensington NSW 2033, Australia

Address at time of publication:
Department of Mathematics, University of Karlstad, S-651 88 Karlstad, Sweden

Email:
genkai.zhang@hks.se

DOI:
https://doi.org/10.1090/S0002-9947-97-01518-3

Keywords:
Bounded symmetric domain,
holomorphic mapping,
Schwarz lemma,
Bergman metric,
Bloch constant

Received by editor(s):
November 21, 1994

Received by editor(s) in revised form:
May 10, 1995

Additional Notes:
Research sponsored by the Australian Research Council

Article copyright:
© Copyright 1997
American Mathematical Society