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2014 Functions of vanishing mean oscillation associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates
The Anh Bui
Tohoku Math. J. (2) 66(2): 269-287 (2014). DOI: 10.2748/tmj/1404911863

Abstract

Let $L$ be a nonnegative self-adjoint operator satisfying Davies-Gaffney estimates on $L^2(X)$, where $X$ is a metric space. In this paper, we introduce and develop a new function space VMO$_{L}(X)$ of vanishing mean oscillation type associated to $L$. We then prove that the dual of VMO$_{L}(X)$ is the Hardy space $H_L(X)$ which was investigated in \cite{HLMMY}. Some characterizations of VMO$_{L}(X)$ are also established.

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The Anh Bui. "Functions of vanishing mean oscillation associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates." Tohoku Math. J. (2) 66 (2) 269 - 287, 2014. https://doi.org/10.2748/tmj/1404911863

Information

Published: 2014
First available in Project Euclid: 9 July 2014

zbMATH: 1298.42026
MathSciNet: MR3229597
Digital Object Identifier: 10.2748/tmj/1404911863

Subjects:
Primary: 42B20
Secondary: 42B25

Rights: Copyright © 2014 Tohoku University

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Vol.66 • No. 2 • 2014
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