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J. Korean Math. Soc. 2016; 53(6): 1391-1409
Online first article August 25, 2016 Printed November 1, 2016
https://doi.org/10.4134/JKMS.j150546
Copyright © The Korean Mathematical Society.
Normality criteria for a family of holomorphic functions concerning the total derivative in several complex variables
Tingbin Cao and Zhixue Liu
Nanchang University, Nanchang University
In this paper, we investigate a family of holomorphic functions in several complex variables concerning the total derivative (or called radial derivative), and obtain some well-known normality criteria such as the Miranda's theorem, the Marty's theorem and results on the Hayman's conjectures in several complex variables. A high-dimension version of the famous Zalcman's lemma for normal families is also given.
Keywords: holomorphic functions, several complex variables, normal family, total derivative
MSC numbers: Primary 30D35; Secondary 32A19, 30D45
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