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

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

15 引文斯高帕斯（Scopus）

摘要

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).

原文	???core.languages.en_GB???
頁（從 - 到）	147-170
頁數	24
期刊	Tohoku Mathematical Journal
卷	57
發行號	2
DOIs	https://doi.org/10.2748/tmj/1119888333
出版狀態	已出版 - 2005

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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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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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EP - 170

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

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Hardy spaces associated to the sections

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