Rate of growth of pth means of invariant potentials in the unit ball of \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: Rate of growth of pth means of invariant potentials in the unit ball of \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0697.31008
DOI: 10.1016/0022-247X(89)90054-1
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Recently, \textit{S. J. Gardiner} [Proc. Am. Math. Soc. 103, No.3, 861-869 (1988; Zbl 0672.31005)] obtained sharp results on the rate of growth of pth means of potentials on the unit ball in \({\mathbb{R}}^ n\). The author proves analogous results for Möbius invariant potentials V on the unit ball in \({\mathbb{C}}^ n\), e.g. if \(1\leq p<(2n-1)/2(n-1)\) then \[ \lim_{r\to 1-}(1-r^ 2)^{n(1-1/p)}[\int_{S}V(rt)^ p d\sigma (t)]^{1/p}=0. \]
Mathematics Subject Classification ID: 31C15
zbMATH DE Number: 4142432
zbMATH Keywords: rate of growth
zbMATH Keywords: pth means
author: Manfred Stoll
reviewed by: Wolfhard Hansen
MaRDI profile type: Publication
cites work: Growth Properties of pth Means of Potentials in the Unit Ball
cites work: Q3922907
cites work: Q3958740
cites work: On the rate of growth of the means \(M^ p\) of holomorphic and pluriharmonic functions on the ball
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: Radial Limits of M-Subharmonic Functions
description: scientific article; zbMATH DE number 4142432