PDE Seminar Abstracts

Differential inequalities and normality

Shahar Nevo
Bar-Ilan University, Ramat Gan, Israel
Mon 27th Feb 2017, 2-3pm, Carslaw Room 829 (AGR)

Abstract

The well known Marty’s theorem asserts that a family F of functions meromorphic in some domain D is normal if and only if for every compact subset K of D there is a positive constant C(K) such that

|f(z)| 1 + |f(z)|2 C(K),

for every f in F and every z in D. We reverse the sign of the inequality and discuss the connection between normality and differential inequalities of the type

|f(k)(z)| h(|f(z)|),

where h is some increasing and continuous function. As we shall see, some of these inequalities imply quasy-normality, a geometric extension of the notion of normality.