A two weight inequality for Calderón–Zygmund operators on spaces of homogeneous type with applications

Let ( X , d , μ ) be a space of homogeneous type in the sense of Coifman and Weiss, i.e. d is a quasi metric on X and μ is a positive measure satisfying the doubling condition. Suppose that u and v are two locally finite positive Borel measures on ( X , d , μ ) . Subject to the pair of weights satisfying a side condition, we characterize the boundedness of a Calderón–Zygmund operator T from L 2 ( u ) to L 2 ( v ) in terms of the A 2 condition …