Maximal commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of homogeneous type

Let X be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, via a new Cotlar type inequality linking commutators and corresponding maximal operators, a weighted L p ( X ) estimate with general weights and a weak type endpoint estimate with A 1 ( X ) weights are established for maximal operators corresponding to commutators of BMO ( X ) functions and singular integral operators with non-smooth kernels.