Vanishing mean oscillation spaces associated with operators satisfying Davies-Gaffney estimates

摘要

Let ( X, d, μ) be a metric measure space, let L be a linear operator that has a bounded H∞-functional calculus and satisfies the Davies--Gaffney estimate, let Φ be a concave function on (0, ∝) of critical lower type p E (0, 1], and let p(t)≡t~(-1)/Φ~(-1) (t-for all t ∈ (0, ∞). In this paper, the authors introduce the generalized VMO space VMOp,L ( X) associated with L and establish its characterization via the tent space. As applications, the authors show that (VMOp,L (X))* Bφ, L( X), where L* denotes the adjoint operator of T in L~2 (X) and Bφ,L * (X) the Banach completion of the Orlicz-Hardy space H_Φ,L * (x ).