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| A Criterion of Normality Concerning Holomorphic Functions Whose Derivative Omits a Function |
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Citation： |
Xiaojun LIU,Yasheng YE.A Criterion of Normality Concerning Holomorphic Functions Whose Derivative Omits a Function[J].Chinese Annals of Mathematics B,2011,32(5):699~710 |
| Page view： 1982
Net amount： 1535 |
Authors： |
Xiaojun LIU; Yasheng YE; |
Foundation： |
the National Natural Science Foundation of China (No. 11071074) and the Outstanding
Youth Foundation of Shanghai (No. slg10015). |
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| Abstract： |
The authors discuss the normality concerning holomorphic functions
and get the following result. Let $\mathcal{F}$ be a family of
holomorphic functions on a domain $D\subset\mathbb C$, all of whose
zeros have multiplicity at least $k$, where $k\ge2$ is an integer.
And let $h(z)\not\equiv0$ be a holomorphic function on $D$. Assume
also that the following two conditions hold for every
$f\in\mathcal{F}$: (a) $f(z)=0\Longrightarrow|f^{(k)}(z)|<|h(z)|$;
(b) $f^{(k)}(z)\ne h(z)$. Then $\mathcal{F}$ is normal on $D$. |
Keywords： |
Normal family, Holomorphic functions, Omitted function |
Classification： |
30D35 |
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