Differential inequalities and a Marty-type criterion for quasi-normality

Jürgen Grahl, Tomer Manket, Shahar Nevo

We show that the family of all holomorphic functions $f$ in a domain $D$ satisfying $$\frac{|f^{(k)}|}{1+|f|}(z)\le C \qquad \mbox{ for all } z\in D$$ (where $k$ is a natural numbe…