Growth and decrease of subharmonic functions in a cone
type: Item
instance of: scholarly article
title: Growth and decrease of subharmonic functions in a cone
zbMATH Open document ID: 0696.31002
DOI: 10.1007/BF01056285
published in: Ukrainian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Consider subharmonic functions in the complex plane. If they satisfy the inequality \[ u(z)\leq a| z|^{\rho}+b;\quad a>0;\quad b\geq 0;\quad \rho >0 \] then Jensen's inequality simply offers integral estimations for u(z) and the corresponding Riesz-measure \(\mu\). The same problem is not trivial for subharmonic functions u(z) belonging to the half-plane and a variety of articles have contributed conditions to derive the desired integral estimations. The author shows that the methods due to literature are also helpful for subharmonic functions in a conus of \(R^ m\) thus generalizing the notion of order of subharmonic functions u(z) in a conus and integral estimations for u(z) and the corresponding Riesz- and surface measures.
Mathematics Subject Classification ID: 31A05
zbMATH DE Number: 4140142
zbMATH Keywords: growth
zbMATH Keywords: decrease
zbMATH Keywords: Jensen's inequality
zbMATH Keywords: Riesz-measure
author: Alexander Rashkovskii
MaRDI profile type: Publication
cites work: AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
cites work: Q3693795
cites work: Q5531193
cites work: Q5535781
cites work: Q3769126
description: scientific article; zbMATH DE number 4140142