Open AccessDuality of multiparameter Hardy spaces Hp on spaces of homogeneous type
Author(s) -
Yongsheng Han,
Ji Li,
Guozhen Lu
Publication year - 2010
Publication title -
annali della scuola normale superiore di pisa. 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