Commutators of BMO functions and singular integral operators with non-smooth kernels

Let X be a space of homogeneous type of infinite measure. Let T be a singular integral operator which is bounded on L-p(X) for some p, 1 < p < infinity. We give a sufficient condition on the kernel of T so that when a function b is an element of BMO(X), the commutator [b, T] (f) = T(bf) - bT(f) is bounded on LP spaces for all p, 1 < p < infinity. Our condition is weaker than the usual Hbrmander condition. Applications include L-p-boundedness of the commutators of BMO functions and holomorphic functional calculi of Schrodinger operators, and divergence form operators on irregular domains.