Convergence of conditional means in the norm of the space BMO
type: Item
instance of: scholarly article
title: Convergence of conditional means in the norm of the space BMO
zbMATH Open document ID: 0726.42006
DOI: 10.1007/BF01057539
author: M. V. Lejbov
published in: Ukrainian Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The author introduces a class of interval \(\sigma\)-algebras on the segment \([0,1].\) These are \(\sigma\)-algebras generated by a countable or finite family \(\{I_ n\}\) of closed intervals \(I_ n\subset [0,1],\) where \(\cup I_ n=[0,1]\) and \(I^ 0_ n\cap I^ 0_ m=\emptyset,\quad n\neq m,\) \(I^ 0\) being the interior of I. He obtains an estimate of the operator norm of the conditional expectation with respect to the interval \(\sigma\)-algebra, acting in the BMO space. The characterization of the VMO space is given in terms of the convergence in the BMO norm of sequences of conditional means with respect to flows of interval \(\sigma\)-algebras with various properties.
Mathematics Subject Classification ID: 42A50
Mathematics Subject Classification ID: 60G46
zbMATH DE Number: 4198745
zbMATH Keywords: interval \(\sigma \) -algebras
zbMATH Keywords: operator norm
zbMATH Keywords: conditional expectation
zbMATH Keywords: BMO space
zbMATH Keywords: VMO space
zbMATH Keywords: convergence
zbMATH Keywords: conditional means
MaRDI profile type: Publication
cites work: Q3329691
cites work: Functions of Vanishing Mean Oscillation
full work available at URL: https://doi.org/10.1007/bf01057539
OpenAlex ID: W2024986906
description: scientific article; zbMATH DE number 4198745