Tohoku Mathematical Journal

Functions of vanishing mean oscillation associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

The Anh Bui

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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.

Article information

Tohoku Math. J. (2), Volume 66, Number 2 (2014), 269-287.

First available in Project Euclid: 9 July 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory

Non-negative self-adjoint operator Hardy space BMO VMO space of homogeneous type


Bui, The Anh. Functions of vanishing mean oscillation associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Tohoku Math. J. (2) 66 (2014), no. 2, 269--287. doi:10.2748/tmj/1404911863.

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