Duality of multiparameter Hardy spaces Hp on spaces of homogeneous type

Abstract

In this paper, we introduce the Carleson measure space CMOp 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].