Duality of multiparameter Hardy spaces 𝐇 𝐩 on spaces of homogeneous type
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 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 ( + 2 × + 2 ) with BMO ( + 2 × + 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
Han, Yongsheng 1 ; Li, Ji 2 ; Lu, Guozhen 3

1 Department of Mathematics, Auburn University, AL 36849-5310, U.S.A
2 Department of Mathematics, ZhongShan University, 510275, China
3 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA
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     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Han, Yongsheng; Li, Ji; Lu, Guozhen. Duality of multiparameter Hardy spaces $\mathbf{H^p}$ on spaces of homogeneous type. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 4, pp. 645-685. http://archive.numdam.org/item/ASNSP_2010_5_9_4_645_0/

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