A remark on BMO and Bloch functions on the unit ball of \(\mathbb{R}^ n\)
type: Item
instance of: scholarly article
title: A remark on BMO and Bloch functions on the unit ball of \(\mathbb{R}^ n\)
zbMATH Open document ID: 0797.31004
author: Miroslav Pavlović
published in: Tokyo Journal of Mathematics
publication date: 1994-04-28T00:00:00Z
review text: Let \(B\) denote the unit ball in \(\mathbb{R}^ n\) \((n\geq 2)\). For a function \(f\) harmonic in \(B\), \(\| f\|_ \beta\) is defined by \[ \| f\|_ \beta= \sup_{x\in B} {\textstyle {1\over2}} (1-| x|^ 2) |\nabla f(x)|. \] It is shown that if \(f\) is harmonic in \(B\) then \[ \| f\|_{\text{BMO}}\leq \sqrt{2} \| f\|_ \beta, \qquad \| f\|_ \beta \leq (n+2)^{1/2} \| f\|_{\text{BMO}}. \] In the proof a simple variant of Green's formula is used.
Mathematics Subject Classification ID: 31B05
zbMATH DE Number: 558838
zbMATH Keywords: Bloch functions
zbMATH Keywords: bounded mean oscillation
reviewed by: Miroslav Dont
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270128484
OpenAlex ID: W2070503443
DOI: 10.3836/TJM/1270128484
description: scientific article; zbMATH DE number 558838