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

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