沿单位方向上的强α型螺形映射的偏差估计

数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 239-247.

沿单位方向上的强α型螺形映射的偏差估计

刘爱超¹, 崔艳艳², 刘浩³

1 黄淮学院数学与统计学院河南驻马店 463000;
2 周口师范学院数学与统计学院河南周口 466001;
3 河南大学数学与统计学院河南开封 475001

收稿日期:2016-06-18 修回日期:2016-12-16 出版日期:2017-04-26 发布日期:2017-04-26
通讯作者: 刘浩 E-mail:liuzefang99@126.com
基金资助:
国家自然科学基金（11271359）和河南省教育厅科学技术研究重点项目（14B110015，14B110016）

The Distortion Estimation for Strongly Spirallike Mappings of Type α Along Unit Direction

Liu Aichao¹, Cui Yanyan², Liu Hao³

1 College of Mathematics and Statistics, Huanghuai University, Henan Zhumadian 463000;
2 College of Mathematics and Statistics, Zhoukou Normal University, Henan Zhoukou 466001;
3 College of Mathematics and Statistics, Henan University, Henan Kaifeng 475001

Received:2016-06-18 Revised:2016-12-16 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the NSFC (11271359) and the Education Department of Henan Science and Technology Key Project (14B110015, 14B110016)

摘要/Abstract

摘要： 各种双全纯映射的偏差估计一直是多复变函数论研究的热点之一.自强α型螺形映射的定义被提出以来，研究人员仅获得了增长与掩盖结果，但对其偏差结果却知之甚少.针对这一情况，利用强α型螺形映射的增长结果，首次获得了复Banach空间中开单位球B及欧式空间中单位多圆柱Dⁿ单位方向上的强α型螺形映射的偏差估计.研究结果使人们对强α型螺形映射的性质有了新的认识.

关键词: 强α型螺形映射, 增长与掩盖定理, 单位方向, 偏差估计

Abstract: Various biholomorphic mappings'distortion estimation have been one of the hot issues studied for the theory of several complex variables. Since the definition of strongly spirallike mappings of type α was presented, the researchers only got growth and covering results, but its distortion estimation have been poorly understood. In response to this situation, we use growth and covering theorem of strongly spirallike mappings of type α, for the first time we obtained the distortion estimation of strongly spirallike mappings of type α in the open unit ball B of a complex Banach spaces and unit polydisc Dⁿ of the European space along unit direction. The results made us have a new understanding for strongly spirallike mappings of type α.

Key words: Strongly spirallike mappings of type α, Growth and covering theorem, Unit direction, Distortion estimation

中图分类号:

O174.56

刘爱超, 崔艳艳, 刘浩. 沿单位方向上的强α型螺形映射的偏差估计[J]. 数学物理学报, 2017, 37(2): 239-247.

Liu Aichao, Cui Yanyan, Liu Hao. The Distortion Estimation for Strongly Spirallike Mappings of Type α Along Unit Direction[J]. Acta mathematica scientia,Series A, 2017, 37(2): 239-247.

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