BOUNDEDNESS OF SINGULAR INTEGRALS AND THEIR COMMUTATORS WITH BMO FUNCTIONS ON HARDY SPACES

In this paper, we establish sufficient conditions for a singular integral T to be bounded from certain Hardy spaces H-L(P) 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-L(1). We then show that our sufficient 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 Schrodinger operator on a Euclidean space, and (iii) T = g(L) is a singular integral operator defined from the holomorphic functional calculus of an operator L or the spectral multiplier of a non-negative self-adjoint operator L.