Duality of multiparameter Hardy spaces Hp on spaces of homogeneous type

Yongsheng Han*, Ji Li, Guozhen Lu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

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 languageEnglish
Pages (from-to)645-685
Number of pages41
JournalAnnali della Scuola Normale - Classe di Scienze
Volume9
Issue number4
Publication statusPublished - 2010
Externally publishedYes

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