Duality of multiparameter Hardy spaces 𝐇 𝐩 on spaces of homogeneous type
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 9 (2010) no. 4, p. 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
@article{ASNSP_2010_5_9_4_645_0,
     author = {Han, Yongsheng and Li, Ji and Lu, Guozhen},
     title = {Duality of multiparameter Hardy spaces $\mathbf{H^p}$ on spaces of homogeneous type},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
     number = {4},
     year = {2010},
     pages = {645-685},
     zbl = {1213.42073},
     mrnumber = {2789471},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2010_5_9_4_645_0}
}
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, Volume 9 (2010) no. 4, pp. 645-685. http://www.numdam.org/item/ASNSP_2010_5_9_4_645_0/

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