Properties of meromorphic \(\varphi \)-normal functions
type: Item
instance of: scholarly article
title: Properties of meromorphic \(\varphi \)-normal functions
zbMATH Open document ID: 1220.30046
author: Rauno Aulaskari
author: Jouni Rättyä
published in: Michigan Mathematical Journal
publication date: 2011-05-23T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 30D45
zbMATH DE Number: 5899026
zbMATH Keywords: normal function
zbMATH Keywords: \(\varphi\)-normal functions
reviewed by: Yinying Kong
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1301586306
OpenAlex ID: W2044632677
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DOI: 10.1307/MMJ/1301586306
description: scientific article; zbMATH DE number 5899026