A criterion of normality based on a single holomorphic function

被引：0
作者：
Xiao Jun Liu
Shahar Nevo
机构：
[1] University of Shanghai for Science and Technology,Department of Mathematics
[2] Bar-Ilan University,Department of Mathematics
来源：
Acta Mathematica Sinica, English Series | 2011年 / 27卷
关键词：
Normal family; holomorphic functions; zero points; 30D45;
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摘要：
Let F be a family of functions holomorphic on a domain D ⊂ ℂ Let k ≥ 2 be an integer and let h be a holomorphic function on D, all of whose zeros have multiplicity at most k −1, such that h(z) has no common zeros with any f ∈ F. Assume also that the following two conditions hold for every f ∈ F: (a) f(z) = 0 ⇒ f′(z) = h(z); and (b) f′(z) = h(z) ⇒ |f(k)(z)| ≤ c, where c is a constant. Then F is normal on D.
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页码：141 / 154
页数：13
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