Hardy spaces associated to the sections

Yong Ding; Chin Cheng Lin

doi:10.2748/tmj/1119888333

Hardy spaces associated to the sections

Yong Ding, Chin Cheng Lin

Department of Mathematics

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

15 Scopus citations

Abstract

In this paper we define the Hardy space H_ℱ¹ (Rⁿ) associated with a family ℱ of sections and a doubling measure μ, where ℱ is closely related to the Monge-Ampère equation. Furthermore, we show that the dual space of H_ℱ¹ (Rⁿ) is just the space BMO_ℱ(Rⁿ), which was first defined by Caffarelli and Gutiérrez. We also prove that the Monge-Ampère singular integral operator is bounded from H_ℱ¹ (Rⁿ) to L1(Rⁿ, dμ).

Original language	English
Pages (from-to)	147-170
Number of pages	24
Journal	Tohoku Mathematical Journal
Volume	57
Issue number	2
DOIs	https://doi.org/10.2748/tmj/1119888333
State	Published - 2005

Keywords

BMO’s
Hardy spaces
Monge-Ampére equation
Singular integral operators

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10.2748/tmj/1119888333

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title = "Hardy spaces associated to the sections",

abstract = "In this paper we define the Hardy space Hℱ1 (Rn) associated with a family ℱ of sections and a doubling measure μ, where ℱ is closely related to the Monge-Amp{\`e}re equation. Furthermore, we show that the dual space of Hℱ1 (Rn) is just the space BMOℱ(Rn), which was first defined by Caffarelli and Guti{\'e}rrez. We also prove that the Monge-Amp{\`e}re singular integral operator is bounded from Hℱ1 (Rn) to L1(Rn, dμ).",

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AU - Ding, Yong

AU - Lin, Chin Cheng

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AB - In this paper we define the Hardy space Hℱ1 (Rn) associated with a family ℱ of sections and a doubling measure μ, where ℱ is closely related to the Monge-Ampère equation. Furthermore, we show that the dual space of Hℱ1 (Rn) is just the space BMOℱ(Rn), which was first defined by Caffarelli and Gutiérrez. We also prove that the Monge-Ampère singular integral operator is bounded from Hℱ1 (Rn) to L1(Rn, dμ).

KW - BMO’s

KW - Hardy spaces

KW - Monge-Ampére equation

KW - Singular integral operators

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DO - 10.2748/tmj/1119888333

M3 - 期刊論文

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SN - 0040-8735

VL - 57

SP - 147

EP - 170

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

IS - 2

ER -

Hardy spaces associated to the sections

Abstract

Keywords

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