Duality of multiparameter Hardy spaces Hp on spaces of homogeneous type

Yongsheng Han; Ji Li; Guozhen Lu

Duality of multiparameter Hardy spaces H^p on spaces of homogeneous type

Yongsheng Han^*, Ji Li, Guozhen Lu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

In this paper, we introduce the Carleson measure space CMO^p 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 language	English
Pages (from-to)	645-685
Number of pages	41
Journal	Annali della Scuola Normale - Classe di Scienze
Volume	9
Issue number	4
Publication status	Published - 2010
Externally published	Yes

Cite this

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title = "Duality of multiparameter Hardy spaces Hp on spaces of homogeneous type",

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].",

author = "Yongsheng Han and Ji Li and Guozhen Lu",

year = "2010",

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pages = "645--685",

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T1 - Duality of multiparameter Hardy spaces Hp on spaces of homogeneous type

AU - Han, Yongsheng

AU - Li, Ji

AU - Lu, Guozhen

PY - 2010

Y1 - 2010

N2 - 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].

AB - 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].

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AN - SCOPUS:79951745478

VL - 9

SP - 645

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JO - Annali della Scuola Normale - Classe di Scienze

JF - Annali della Scuola Normale - Classe di Scienze

SN - 0391-173X

IS - 4

ER -

Duality of multiparameter Hardy spaces H^p on spaces of homogeneous type

Abstract

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