多复变数星形映射在某方向上精确的偏差定理On the precise distortion theorems for starlike mappings along a unit direction in several complex variables
卢金;刘太顺;王俊;
摘要(Abstract)：
研究了Cn中单位多圆柱上星形映射在某方向上精确的偏差定理.给出了复Banach空间单位球的某方向上精确的偏差的上界,同时给出了下界的猜测.
关键词(KeyWords)： 星形映射;偏差定理;增长定理
基金项目(Foundation): 国家自然科学基金(11101139,11261022,11031008);; 浙江省新苗计划;; 湖师院科研项目(KX21057)
作者(Authors): 卢金;刘太顺;王俊;
参考文献(References)：
- [1]Duren P L.Univalent Function[M].Berlin:Springer-Verlag,1983.
- [2]龚昇.多复变数的凸映照和星形映照[M].2版.北京:科学出版社,2003.
- [3]殷承元.多复变数的二阶微分从属[J].纯粹数学与应用数学,2003,19(1):83-87.
- [4]Barnard R W,FitzGeral C H,Gong S.A distortion theorem for biholomorphic mappings in C2[J].Trans.Amer.Math.Soc.,1994,344:902-924.
- [5]Gong S,Wang S K,Yu Q H.Biholomorphic convex mappings of ball in C2[J].Pacific J.Math.,1993,161(2):287-306.
- [6]Gong S,Liu T S.Distortion theorems for biholomorphic convex mappings on bounded convex circular domains[J].Chin.Ann.of Math.,1999,20B(3):297-304.
- [7]Liu T S,Zhang W J.A distortion theorem of biholomorphic convex mappings in a Banach space[J].Acta.Math.Sinica.,2003,46A(6):1041-1046.
- [8]Graham I,Varolin D.Bloch constants in one and several variables[J].Pacific J.Math.,1996,174:347-357.
- [9]T Honda.The growth theorem for k-fold symmetric convex mappings[J].Bull London Math.Soc.,2002,34:717-724.
- [10]Liu T S,Liu X S.On the precise growth,covering,and distortion theorems for normalized biholomorphic mappings[J].J.Math.Anal.appl.,2004,295:404-417.
- [11]Liu T S,Wang J F,Lu J.Distortion theorems of starlike mappings along a unit direction in Cn[J].Taiwanese J.Math.,2011,15(6):2601-2608.