In this paper, we introduce the Carleson measure space 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 of two homogeneous spaces defined in [15]. Our results thus extend the duality theory of Chang and R. Fefferman [2,3] on with 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].
@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}, pages = {645--685}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 9}, number = {4}, year = {2010}, mrnumber = {2789471}, zbl = {1213.42073}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2010_5_9_4_645_0/} }
TY - JOUR AU - Han, Yongsheng AU - Li, Ji AU - Lu, Guozhen TI - Duality of multiparameter Hardy spaces $\mathbf{H^p}$ on spaces of homogeneous type JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 645 EP - 685 VL - 9 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2010_5_9_4_645_0/ LA - en ID - ASNSP_2010_5_9_4_645_0 ER -
%0 Journal Article %A Han, Yongsheng %A Li, Ji %A Lu, Guozhen %T Duality of multiparameter Hardy spaces $\mathbf{H^p}$ on spaces of homogeneous type %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 645-685 %V 9 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2010_5_9_4_645_0/ %G en %F 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, Tome 9 (2010) no. 4, pp. 645-685. http://www.numdam.org/item/ASNSP_2010_5_9_4_645_0/
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