NORMALITY CRITERIA FOR A FAMILY OF HOLOMORPHIC FUNCTIONS CONCERNING THE TOTAL DERIVATIVE IN SEVERAL COMPLEX VARIABLES

Tingbin Cao, Zhixue Liu
2016 Journal of the Korean Mathematical Society  
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.
doi:10.4134/jkms.j150546 fatcat:lqqyt52v2rhd3iygjdu6zrebwu