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.
Citation
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
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