On a BMO-property for subharmonic functions
type: Item
instance of: scholarly article
title: On a BMO-property for subharmonic functions
zbMATH Open document ID: 1027.31002
author: Alexander Brudnyi
published in: The Journal of Fourier Analysis and Applications
publication date: 2004-01-07T00:00:00Z
review text: A compact set \(K\subset \mathbb{R}^2\) is called (Ahlfors) \(d\)-regular, if there exists \(a>0\) such that for any \(x\in K\) and \(0<t\leq \text{diam}(K)\) \[ \mathcal{H}^d(K_{x,t})\leq at^d \] where \(K_{x,t}=\{z\in \mathbb{C}: |x-z|<t\}\cap K\) and \(\mathcal{H}^d(\omega)\) stands for the \(d\)-Hausdorff measure of \(\omega\). If also \(bt^d \leq \mathcal{H}^d(K_{x,t})\), then the set \(K\) is said to be a \(d\)-set. The author proves that, for any subharmonic function defined on an open neighbourhood of \(K\), its restriction \(f|_{K}\) belongs to \(\text{BMO}(K, \mathcal{H}^d)\).
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1921139
zbMATH Keywords: subharmonic functions
zbMATH Keywords: Ahlfors regular sets
zbMATH Keywords: d-regular sets
zbMATH Keywords: BMO-functions
reviewed by: S. G. Samko
MaRDI profile type: Publication
full work available at URL: s00041-002-0029-y
OpenAlex ID: W2063419230
DOI: 10.1007/S00041-002-0029-Y
description: scientific article; zbMATH DE number 1921139