多复变数准凸映射的偏差定理  

Distortion Theorems of Quasi-convex Mappings in Several Complex Variables

作　　者：刘太顺[1] 卢金[1] 王建飞[2] 

机构地区：[1]湖州师范学院数学系,浙江湖州313000 [2]浙江师范大学数理信息学院,浙江金华321004

出　　处：《数学年刊（A辑）》2011年第5期607-612,共6页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10971063;No.11001246;No.11031008;No.11101139);浙江省自然科学基金(No.D7080080;No.Y6090694;No.Y6110260;No.Y6110053;No.Y6090036;No.Y6100219)资助的项目

摘　　要：首先给出了C^n中单位多圆柱D^n上准凸映射f关于Jacobin矩阵J_f(z)的偏差定理.该定理是单位圆盘凸函数的偏差定理在多复变中的推广.其次得到了Banach空间单位球上准凸映射的偏差定理的上界.最后给出了关于准凸映射偏差定理的两个猜想.Firstly,the authors are concerned with the distortion theorem for the Jacobian matrix J_f（z） in the case of quasi-convex mapping f on the unit polydisc D^n in C^n.The result is a new generalization to the case of several complex variables of the well-known distortion theorem for convex functions of the unit disc.Secondly,the authors obtain the upper bound estimate of the distortion theorem for quasi-convex mappings on the unit ball of a complex Banach space.Finally,two conjectures are given for quasi-convex mappings on the unit polydisc as well as on the unit ball of a complex Banach space.

关 键 词：准凸映射 偏差定理 增长定理 BANACH空间 

分 类 号：O174.56[理学—数学]