Duality of multiparameter Hardy spaces Hp on spaces of homogeneous type | Zendy

Yongsheng Han | Zendy; Ji Li | Zendy; Guozhen Lu | Zendy

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Duality of multiparameter Hardy spaces Hp on spaces of homogeneous type

Author(s) -

Yongsheng Han,

Ji Li,

Guozhen Lu

Publication year - 2010

Publication title -

annali scuola normale superiore - classe di scienze

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.444

H-Index - 37

eISSN - 2036-2145

pISSN - 0391-173X

DOI - 10.2422/2036-2145.2010.4.01

Subject(s) - hardy space , mathematics , duality (order theory) , homogeneous , pure mathematics , space (punctuation) , type (biology) , hilbert space , product (mathematics) , measure (data warehouse) , dual (grammatical number) , mathematical analysis , combinatorics , computer science , geometry , art , ecology , literature , database , biology , operating system

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₊ x ℝ²₊) with BMO(ℝ²₊ x 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].41 page(s

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