Duality of multiparameter Hardy spaces ${𝐇}^{𝐩}$ on spaces of homogeneous type

Han, Yongsheng; Li, Ji; Lu, Guozhen

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 4, pp. 645-685

In this paper, we introduce the Carleson measure space ${\mathrm{CMO}}^p$ 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 $H^1({ℝ}_{+}^2\times {ℝ}_{+}^2)$ with $\mathrm{BMO}({ℝ}_{+}^2\times {ℝ}_{+}^2)$ 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].

Classification : 42B30, 42B35, 46B45

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