Hardy Spaces Associated with Non-negative Self-adjoint Operators and Ball Quasi-Banach Function Spaces on Doubling Metric Measure Spaces and Their Applications

Let (chi, d, mu) be a doubling metric measure space in the sense of R. R. Coifman and G. Weiss, L a non-negative self-adjoint operator on L-2(chi) satisfying the Davies-Gaffney estimate, and chi(chi) a ball quasi-Banach function space on X satisfying some extra mild assumptions. In this article, the authors introduce the Hardy type space H-X, (L) (chi) by the Lusin area function associated with L and establish the atomic and the molecular characterizations of H-X,H- L (chi). As an application of these characterizations of H-X,H- L (chi), the authors obtain the boundedness of spectral multiplies on H-X,H- L (chi). Moreover, when L satisfies the Gaussian upper bound estimate, the authors further characterize H-X,H- L (chi) in terms of the Littlewood-Paley functions g(L) and g(lambda), (*)(L) and establish the boundedness estimate of Schrodinger groups on H-X,H- L (chi). Specific