调和函数在多重L算子作用下的单叶半径估计  

Estimates on the Univalent Radius for Harmonic Mappings under Multiple Differential Operators

作　　者：王其文[1] 黄心中[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《漳州师范学院学报（自然科学版）》2013年第1期9-18,共10页Journal of ZhangZhou Teachers College（Natural Science)

基　　金：福建省自然科学基金资助项目(2011J0101)

摘　　要：若f(z)为定义在单位圆盘D={z||z|<1}上的调和函数,L=z(/z)(/z)为微分算子.本文研究在调和函数f(z)的系数模满足两个著名猜想及某些系数模界限条件下,多重L算子作用于f(z)下的单叶半径估计问题,分别得到相应的精确单叶半径表达式.Suppose that f（z） is a harmonic mapping on the unit disk D={z｜｜z｜〈1}. Let L represents the differential operator L=zd/di-d/ . In this note, we obtain several sharp estimates on univalent radii for the harmonic mappings that are obtained by multiple differential operators L acting on the given harmonic mapping f（z） with its coefficients satisfying two famous conjecture bounds and some general expression bound.

关 键 词：调和函数 微分算子 单叶半径 系数界限 

分 类 号：O174[理学—数学]