SUBCLASSES OF BIHOLOMORPHIC MAPPINGS UNDER THE EXTENSION OPERATORS

doi:10.1007/s10473-019-0122-9

Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (1): 297-311.doi: 10.1007/s10473-019-0122-9

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SUBCLASSES OF BIHOLOMORPHIC MAPPINGS UNDER THE EXTENSION OPERATORS

Chaojun WANG¹, Yanyan CUI^1,2, Hao LIU³

1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China;
3. Institute of Contemporary Mathematics, Henan University, Kaifeng 475001, China

Received:2016-12-04 Revised:2017-09-15 Online:2019-02-25 Published:2019-03-13
Contact: Hao LIU E-mail:haoliu@henu.edu.cn
Supported by:
This work was supported by NSF of China (11271359, 11471098), Science and Technology Research Projects of Henan Provincial Education Department (19B110016), Scientific Research Innovation Fund Project of Zhoukou Normal University (ZKNUA201805).

Abstract

Abstract: In this article, we mainly study the invariance of some biholomorphic mappings with special geometric characteristics under the extension operators. First we generalize the Roper-Suffridge extension operators on Bergman-Hartogs domains. Then, by the geometric characteristics of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of S_Ω^*Ω(β, A, B), parabolic and spirallike mappings of type β and order ρ, strong and almost spirallike mappings of type β and order α as well as almost starlike mappings of complex order λ on Ω_p1^Bⁿ,…,p_s,q under different conditions, respectively. The conclusions provide new approaches to construct these biholomorphic mappings in several complex variables.

Key words: spirallike mappings, Roper-Suffridge operator, Bergman-Hartogs domains

Chaojun WANG, Yanyan CUI, Hao LIU. SUBCLASSES OF BIHOLOMORPHIC MAPPINGS UNDER THE EXTENSION OPERATORS[J].Acta mathematica scientia,Series B, 2019, 39(1): 297-311.

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SUBCLASSES OF BIHOLOMORPHIC MAPPINGS UNDER THE EXTENSION OPERATORS

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