Spread of functions meromorphic in the disc
type: Item
instance of: scholarly article
title: Spread of functions meromorphic in the disc
zbMATH Open document ID: 0749.30019
DOI: 10.1007/BF01102490
author: I. I. Marchenko
author: A. I. Shcherba
published in: Journal of Soviet Mathematics
publication date: 1992-09-26T00:00:00Z
review text: Let \(f\) be a function meromorphic in the unit disc. The paper contains estimations from below for the upper limits (as \(r\to 1)\) of the following quantities: \[ (1-r)^{-1}\text{ mes}(t:\log| f(re^{it})|>qT(r,f)/(1-r)), \] \[ (1-r)^{-1}\text{ mes}(t:\log| f(re^{it})|>qT(r,f)), \] \[ (1-r)^{-1}\text{ mes}(t:\log| f(re^{it})|>q \log M(r,f)), \] where \(0\leq q<\infty\); \(T\) and \(M\) are standard notations of the Nevanlinna theory. These estimations are obtained in terms of the lower order of the function \(f\) and the quantities \(\delta(\infty,f)\), \(\beta(\infty,f)\), \(\hat\beta(\infty,f)\), where \(\delta\) is the Nevanlinna deficiency and the \(\beta\)'s are the Petrenko deviations [\textit{V. P. Petrenko}, Entire curves (Russian) (1984; Zbl 0591.30030)].
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 56614
zbMATH Keywords: Baernstein's star-function
zbMATH Keywords: estimations from below
zbMATH Keywords: lower order
zbMATH Keywords: Nevanlinna deficiency
zbMATH Keywords: Petrenko deviations
reviewed by: I. V. Ostrovskii
MaRDI profile type: Publication
cites work: Sums of deficiencies of meromorphic functions
cites work: Proof of Edrei's Spread Conjecture
cites work: The Size of the Set on Which a Meromorphic Function is Large
cites work: Q3719007
cites work: Q3473349
cites work: Q3792949
description: scientific article; zbMATH DE number 56614