Duality of multiparameter Hardy spaces H^p on spaces of homogeneous type

In this paper, we introduce the Carleson measure space CMO^p on product spaces of homogeneous type in the sense of Coifman and Weiss [4], and prove that it is the dual space of the product Hardy space H p of two homogeneous spaces defined in [15]. Our results thus extend the duality theory of Chang and R. Fefferman [2, 3] on H¹(ℝ² ₊ × ℝ² ₊) with BMO(ℝ² ₊ × ℝ² ₊) which was established using bi-Hilbert transform. Our method is to use discrete Littlewood-Paley analysis in product spaces recently developed in [13] and [14].