The Bloch theorem in several complex variables
Copyright policy )The Bloch theorem in several complex variables
The background theory for the Bloch Theorem is generalized to classical domains in several complex variables. In particular, the Bergman kernel function is used to extend work of Landau and Bonk. The principal conclusion of the paper is the lower estimate for Bloch's constant for mappings of \(n \times m\) matrix domains that are the first type of classical domain. In case that \(m=1\), the results specialize to the estimate given for the \(n\)-dimensional ball given by Liu recently. In case that both \(n=1\) and \(m=1\), the estimate coincides with that given much earlier by Ahlfors.
- University of California, San Diego United States
- University of Science and Technology of China China (People's Republic of)
- University of California, San Diego United States
classical domains, Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube), Integral representations; canonical kernels (Szegő, Bergman, etc.), Bloch's constant, Other generalizations of function theory of one complex variable, Bergman kernel function, Normal functions of one complex variable, normal families, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
classical domains, Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube), Integral representations; canonical kernels (Szegő, Bergman, etc.), Bloch's constant, Other generalizations of function theory of one complex variable, Bergman kernel function, Normal functions of one complex variable, normal families, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
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