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].
Original language | English |
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Pages (from-to) | 645-685 |
Number of pages | 41 |
Journal | Annali della Scuola Normale - Classe di Scienze |
Volume | 9 |
Issue number | 4 |
Publication status | Published - 2010 |
Externally published | Yes |