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arXiv · 1608.04947

Quasi-normality induced by differential inequalities

Jürgen Grahl·Shahar Nevo
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Abstract

We show that the family ${\cal F}_k$ of all meromorphic functions $f$ in a domain $D$ satisfying $$\frac{|f^{(k)}|}{1+|f|}(z)\ge C \qquad \mbox{ for all } z\in D$$ (where $k$ is a natural number and $C>0$) is quasi-normal. The proof relies mainly on the Zalcman-Pang rescaling method.

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Jürgen Grahl, Shahar Nevo. 2016-08-17. Quasi-normality induced by differential inequalities. https://doi.org/10.1112/blms.12111

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