Discrete Littlewood-Paley-Stein theory and multi-parameter Hardy spaces associated with flag singular integrals

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dc.creatorHan, Yongsheng
dc.creatorLu, Guozhen
dc.date2008-01-11
dc.date.accessioned2026-07-07T08:53:46Z
dc.date.available2026-07-07T08:53:46Z
dc.descriptionThe main purpose of this paper is to develop a unified approach of multi-parameter Hardy space theory using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the goal to establish and develop the Hardy space theory for the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. This approach enables us to avoid the use of transference method of Coifman-Weiss as often used in the $L^p$ theory for $p>1$ and establish the Hardy spaces $H^p_F$ and its dual spaces associated with the flag singular integral operators for all $0<p\leq 1$. We also prove the boundedness of flag singular integral operators on $BMO_F$ and $H^p_F$, and from $H^p_F$ to $L^p$ for all $0<p\le 1$ without using the deep atomic decomposition. As a result, it bypasses the use of Journe's type covering lemma in this implicit multi-parameter structure. The method used here provides alternate approaches of those developed by Chang, R. Fefferman, Journe and Pipher in the pure product setting. A Calderon-Zygmund decomposition and interpolation theorem are also proved for the implicit multi-parameter Hardy spaces.
dc.description50 pages
dc.identifierhttps://arxiv.org/abs/0801.1701
dc.identifierhttp://arxiv.org/abs/0801.1701
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145740
dc.subjectClassical Analysis and ODEs
dc.subject42B30; 42B35
dc.titleDiscrete Littlewood-Paley-Stein theory and multi-parameter Hardy spaces associated with flag singular integrals
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