Functions of vanishing mean oscillation associated with operators and applications
type: Item
instance of: scholarly article
title: Functions of vanishing mean oscillation associated with operators and applications
zbMATH Open document ID: 1158.32002
author: Donggao Deng
author: Xuan Thinh Duong
author: Liang Song
author: Chaoqiang Tan
author: Lixin Yan
published in: Michigan Mathematical Journal
publication date: 2009-02-20T00:00:00Z
review text: The authors introduce new function spaces \(\mathbf{VMO}_L (\mathbb{R}^n)\) of vanishing mean oscillation associated with infinitesimal generators of analytic semigroups on \(L^2 (\mathbb{R}^n)\). Such spaces generalize the classical \(\mathbf{VMO}\) space. Let \(L^*\) denote the adjoint of the operator \(L\). The main result of the paper is that under some conditions imposed on the operator \(L\), the dual of the space \(\mathbf{VMO}_{L^*} (\mathbb{R}^n)\) coincides with the Hardy space \(H^1_L(\mathbb{R}^n)\). Moreover, a number of spaces \(\mathbf{VMO}_L (\mathbb{R}^n)\) generated by specific differential operators \(L\) are considered and relations to the classic \(\mathbf{VMO}(\mathbb{R}^n)\) and to other relevant spaces are presented.
Mathematics Subject Classification ID: 32A37
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 5509671
zbMATH Keywords: vanishing mean oscillation
zbMATH Keywords: function space
zbMATH Keywords: duality
reviewed by: Victor D. Didenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1231770358
OpenAlex ID: W1968363135
cites work: Q4217284
cites work: Remarks on some subspaces of BMO(\({\mathbb R}^n\)) and of bmo(\({\mathbb R}^n\)).
cites work: Functional calculus on \(BMO\) and related spaces
cites work: Q3036043
cites work: Some new function spaces and their applications to harmonic analysis.
cites work: Extensions of Hardy spaces and their use in analysis
cites work: On a generalized Carleson inequality
cites work: New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications
cites work: Duality of Hardy and BMO spaces associated with operators with heat kernel bounds
cites work: \(H^p\) spaces of several variables
cites work: On functions of bounded mean oscillation
cites work: Q5708176
cites work: Functions of Vanishing Mean Oscillation
cites work: Q3142876
cites work: On the compactness of operators of Hankel type
cites work: Q4141653
DOI: 10.1307/MMJ/1231770358
description: scientific article; zbMATH DE number 5509671