一类准凸映照族的偏差定理及de la Vallée Poussin均值  

Distortion theorem and de la Vallée Poussin means for a class of quasi-convex mappings

作　　者：徐庆华[1] 刘太顺[2] XU QingHua LIU TaiShun

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022 [2]湖州师范学院理学院,湖州313000

出　　处：《中国科学：数学》2016年第11期1691-1702,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11561030,11471111和11261022);江西省自然科学基金(批准号:20152ACB20002)资助项目

摘　　要：本文建立了一类准凸映照族的Fréchet导数型和行列式型偏差定理.同时,本文将单位圆盘上凸函数的de la Vallée Poussin均值性质推广到高维空间,所得结果是单复变中的经典结论在多复变中的拓广.Abstract In this paper, we establish distortion theorems of the FrSchet derivative and the Jacobi determinant for the subclass of biholomorphic mappings in several complex variables, which is another extension to higher dimensions of the normalized convex functions on the unit disc U in C. Meanwhile, the de la Vallee Poussin means for convex functions on U can be extended to this class of mappings on the Euclidean unit ball. The results presented here would generalize some classical results in one complex variable.

关 键 词：D型准凸映照族 偏差定理 DE LA Vallee Poussin均值 

分 类 号：O174[理学—数学]