In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of ...In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.展开更多
In this paper, we give a property of normalized biholomorphic convex mappings on the first, second and third classical domains: for any Z0 belongs to the classical domains,f maps each neighbourhood with the center Z0,...In this paper, we give a property of normalized biholomorphic convex mappings on the first, second and third classical domains: for any Z0 belongs to the classical domains,f maps each neighbourhood with the center Z0, which is contained in the classical domains,to a convex domain.展开更多
1. In Ref. [1], Carl H. FitzGerald et al. gave the first result about the growth theorem in several complex variables. They proved that if f is a normalized biholomorphic starlike mapping from the unit ball B^n to C^n,
基金supported by National Natural Science Foundation of China (10871145 10926066)+1 种基金Doctoral Program Foundation of the Ministry of Education of China (20090072110053)Natural Science Foundation of Zhejiang Province (Y6100007)
文摘In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.
基金Foundation item： Supported by the National Natural Science Foundation of China（11001074, 11061015, 11101124）
文摘In this paper, we give a property of normalized biholomorphic convex mappings on the first, second and third classical domains: for any Z0 belongs to the classical domains,f maps each neighbourhood with the center Z0, which is contained in the classical domains,to a convex domain.
文摘1. In Ref. [1], Carl H. FitzGerald et al. gave the first result about the growth theorem in several complex variables. They proved that if f is a normalized biholomorphic starlike mapping from the unit ball B^n to C^n,
