调和函数类的一些界的估计结果  

Some Bounds for a Family of Harmonic Mappings

作　　者：熊良鹏 王雅倩 XIONG Liangpeng;WANG Yaqian(School of Mathematics and Computer Science,Jiangxi Science and Technology Normal University,Nanchang 330038,China)

机构地区：[1]江西科技师范大学数学与计算机科学学院,南昌330038

出　　处：《数学年刊（A辑）》2022年第4期431-444,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.12061035);江西省自然科学基金(No.20212BAB201012);江西省教育厅科研项目(No.GJJ201104);江西科技师范大学青年拔尖人才项目(No.2021QNBJRC003)的资助。

摘　　要：研究了单位开圆盘内保向复值的调和函数类,其中函数的解析部分满足一定的从属条件.完整的给出了该函数类Bloch常数的界、系数估计、增长和偏差不等式的界.进一步,通过指定一些关键参数,证明其pre-Schwarzian导数的范数也是有界的.In this paper,the authors introduce a class of the sense-preserving complexvalued harmonic functions f in open unit disk,and the analytic parts of f are restricted to subordinate a fractional function whose image is symmetric with respect to the real axis.With this class,the authors obtain the bounds on Bloch constant,coefficients estimates,growth and distortion theorems.By specifying some crucial parameters,the authors also prove that the norm of pre-Schwarzian derivative for the class is bounded.

关 键 词：BLOCH常数 偏差定理 调和函数 Janowsk凸函数 pre-Schwarzian导数 

分 类 号：O174.51[理学—数学]