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

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 VMOL (X) of vanishing mean oscillation type associated to L. We then prove that the dual of VMOL (X) is the Hardy space H-L (X) which was investigated in [18]. Some characterizations of VMOL (X) are also established.