Properties of meromorphic \(\varphi \)-normal functions
This paper shows some properties of meromorphic \(\varphi\)-normal functions. The authors study subsets of \(M(D)\) which are defined by the condition \(f^\sharp(z)=O\big(\varphi(|z|)\big)\) as \(|z|\rightarrow 1^-\), where the function \(\varphi(r)\) admits a sufficient regularity near \(1\) and exceeds \(1/(1-r^2)\) in growth. Those sets are larger than the class \(N\) of normal functions, and their members are called \(\varphi\)-normal functions. Finally, they illustrate what it means to change the growth restriction of spherical derivatives from \(1/(1-|z|^2)\) of normal functions to \(\varphi(|z|)\) of \(\varphi\)-normal functions.
scientific article; zbMATH DE number 5899026
scientific article