Boundedness of singular integrals and their commutators with BMO functions on hardy spaces

In this paper, we establish suffcient conditions for a singular integral T to be bounded from certain Hardy spaces H^p _L to Lebesgue spaces L^p, 0 < p (≤ 1, and for the commutator of T and a BMO function to be weak-type bounded on Hardy space H(¹ _L. We then show that our suffcient conditions are applicable to the following cases: (i) T is the Riesz transform or a square function associated with the Laplace- Beltrami operator on a doubling Riemannian manifold, (ii) T is the Riesz transform associated with the magnetic Schrödinger operator on a Euclidean space, and (iii) T = g(L) is a singular integral operator deffned from the holomorphic functional calculus of an operator L or the spectral multiplier of a non-negative self-adjoint operator L.