SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

doi:10.1007/s10473-022-0202-0

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 454-466.doi: 10.1007/s10473-022-0202-0

SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

刘小松

School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, China

收稿日期:2020-02-26 出版日期:2022-04-25 发布日期:2022-04-22
作者简介:Xiaosong LIU,E-mail:lxszhjnc@163.com
基金资助:
Supported by National Natural Science Foundation of China (11871257, 12071130).

SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

Xiaosong LIU

School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, China

Received:2020-02-26 Online:2022-04-25 Published:2022-04-22
Supported by:
Supported by National Natural Science Foundation of China (11871257, 12071130).

摘要/Abstract

摘要： In this paper, we first establish the sharp growth theorem and the distortion theorem of the Frechét derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in Cⁿ with some restricted conditions. We next give the distortion theorem of the Jacobi determinant for biholomorphic mappings defined on the unit ball of Cⁿ with an arbitrary norm and the unit polydisk in Cⁿ under certain restricted assumptions. Finally we obtain the sharp Goluzin type distortion theorem for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in Cⁿ with some additional conditions. The results derived all reduce to the corresponding classical results in one complex variable, and include some known results from the prior literature.

关键词: Biholomorphic mapping, distortion theorem, Frechét derivative, Jacobi determinant, Goluzin type distortion theorem

Abstract: In this paper, we first establish the sharp growth theorem and the distortion theorem of the Frechét derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in Cⁿ with some restricted conditions. We next give the distortion theorem of the Jacobi determinant for biholomorphic mappings defined on the unit ball of Cⁿ with an arbitrary norm and the unit polydisk in Cⁿ under certain restricted assumptions. Finally we obtain the sharp Goluzin type distortion theorem for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in Cⁿ with some additional conditions. The results derived all reduce to the corresponding classical results in one complex variable, and include some known results from the prior literature.

Key words: Biholomorphic mapping, distortion theorem, Frechét derivative, Jacobi determinant, Goluzin type distortion theorem

中图分类号:

32A30

刘小松. SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES[J]. 数学物理学报(英文版), 2022, 42(2): 454-466.

Xiaosong LIU. SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES[J]. Acta mathematica scientia,Series B, 2022, 42(2): 454-466.

参考文献

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SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

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