Inhomogeneous Calderón reproducing formula on spaces of homogeneous type

In this paaper we use the Calderón-Zygmund operator theory to prove an inhomogenous Calderón reproducing formula on spaces of homogeneous type with finite or infinite measures. Our formula is new even for classical spaces of homogeneous type such as the surface of the unit ball and then-torus inR ⁿ, compact Lie groups,C ^∞-compact Riemannian manifolds, and the boundary of any bounded Lipschitz domain inR ⁿ.