Commutators of Calderon-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrodinger operators

Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator T (b) f = bT f - T(bf) on L (p) , p a (1,a), where T is a Caldern-Zygmund operator related to the admissible function rho and b a BMO (theta) (X) aS double dagger BMO(X). Moreover, they prove that T (b) is bounded from the Hardy space H (rho) (1) (X) into the weak Lebesgue space L (weak) (1) (X). This can be used to deal with the Schrodinger operators and Schrodinger type operators on the Euclidean space a"e (n) and the sub-Laplace Schrodinger operators on the stratified Lie group G.