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Normality criteria for a family of holomorphic functions concerning the total derivative in several complex variables

Zhixue Liu|Ting-Bin Cao
대한수학회 (The Korean Mathematical Society)|2016.11|대한수학회지 (Journal of the KMS)|제53권 제6호|pp. 1391-1409

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참고문헌

키워드

normal familyholomorphic functionsseveral complex variablestotal derivative
주제분류수학

초록

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.

Abstract

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.

참고문헌 (37)

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