| A NECESSARY AND SUFFICIENT CONDITION THAT BIHOLOMORPHIC MAPPINGS ARE STARLIKE ON A CLASS OF REINHARDT DOMAINS |
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| 作者姓名： | Gong Sheng |
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| 作者单位： | Department of Mathematics University of Science and Technology of China，Hefei，Anhui 230026，Institute of Applied Mathematics，Academia Sinica，Beijing 100080，China.，Institute of Applied Mathematics，Academia Sinica，Beijing 100080，China. |
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| 基金项目： | Projects supported by the National Natuzal Science Foundation of China |
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| 摘 要： | This paper studies the Reinhardt domains B defined as(?)The Schwartz lemma for B is established.Using it the authors give a necessary andsu fficient condition that a local biholomorphic mapping from B to C~n is starlike.It isreduced to the Suffridge's theorem in the case p_1=p_2=…=p_n>1.
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| 收稿时间： | 1990/3/13 0:00:00 |
A NECESSARY AND SUFFICIENT CONDITION THAT BIHOLOMORPHIC MAPPINGS ARE
STARLIKE ON A CLASS OF REINHARDT DOMAINS |
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| Institution: | Department of Mathematics, University of Science and Technology of China, Hefei, Anhui,230026.,Department of Mathematics, University of Science and Technology of China, Hefei, Anhui,230026. and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui,230026. |
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| Abstract: | This paper studies the Reinhardt domains B defined as
$B \equiv{Z=(\z_1,\z_2,\cdots,\z_n \in C^n|\\sum\limits_{i = 1}^n {|{z_i}{|^{{p_i}}} < 1} \],2p_n>p_1\geq p_2\geq \cdots \geq p_n >1.}$
The Schwartz lemma for B is established. Using it the authors give a necessary aad sufficient condition that a local biholomorphic mapping from B to $C^n$ is starlike. It is reduced to the Suffridge's theorem in the case $p_1=p_2=\cdots=p_n>1$. |
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