FUNCTIONS OF VANISHING MEAN OSCILLATION ASSOCIATED TO NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING DAVIES-GAFFNEY ESTIMATES

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 [18]. Some characterizations of VMO$_L(X)$ are also established.