Uniform limits of Green potentials in the unit disc
type: Item
instance of: scholarly article
title: Uniform limits of Green potentials in the unit disc
zbMATH Open document ID: 0727.31001
DOI: 10.1007/BF01190082
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: In a previous work [Proc. Am. Math. Soc. 93, 567-568 (1985; Zbl 0561.31003)] the author proved the following: Theorem A. If \(G_{\mu}\) is the Green potential of a measure \(\mu\) satisfying \(\int_{D}(1-| z|)d\mu (z)<\infty\) then \((1)\quad \liminf_{r\to 1^-}(1-r)M_{\infty}(G_{\mu},r)=0,\) where \(M_{\infty}(G_{\mu},r)=\sup_{| z| =r}G_{\mu}(z).\) This paper proves a variation of (1) where the weight function is \((1- r)^{\alpha}\), \(0\leq \alpha \leq 1\). Then it provides sufficient conditions that guarantee that the limit in (1) is zero, rather than just the limit inferior.
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 31A20
zbMATH DE Number: 4200576
zbMATH Keywords: uniform limits
zbMATH Keywords: Green potential
author: Manfred Stoll
MaRDI profile type: Publication
cites work: Q4039801
cites work: Growth Properties of pth Means of Potentials in the Unit Ball
cites work: The minimum modulus of a bounded analytic function
cites work: Boundary Behavior of Green Potentials
cites work: Shorter Notes: Boundary Limits of Subharmonic Functions in the Disc
cites work: Boundary limits of Green potentials in the unit disc
cites work: Rate of growth of pth means of invariant potentials in the unit ball of \({\mathbb{C}}^ n\)
cites work: Limiting Values of Subharmonic Functions
cites work: On multipliers preserving convergence of trigonometric series almost everywhere
full work available at URL: https://doi.org/10.1007/bf01190082
OpenAlex ID: W2090985194
description: scientific article; zbMATH DE number 4200576