Boundedness of Monge-Ampére singular integral operators acting on hardy spaces and their duals

Chin Cheng Lin

doi:10.1090/tran/6397

Boundedness of Monge-Ampére singular integral operators acting on hardy spaces and their duals

Chin Cheng Lin

Department of Mathematics

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

7 Scopus citations

Abstract

We study the Hardy spaces H_F^p associated with a family F of sections which is closely related to the Monge-Ampére equation. We characterize the dual spaces of H_F^p, which can be realized as Carleson measure spaces, Campanato spaces, and Lipschitz spaces. Also the equivalence between the characterization of the Littlewood-Paley g-function and atomic decomposition for H_F^p is obtained. Then we prove that Monge-Ampére singular operators are bounded from H_F^p into L_μ^p and bounded on both H_F^p and their dual spaces.

Original language	English
Pages (from-to)	3075-3104
Number of pages	30
Journal	Transactions of the American Mathematical Society
Volume	368
Issue number	5
DOIs	https://doi.org/10.1090/tran/6397
State	Published - May 2016

Keywords

Campanato spaces
Carleson measure spaces
Hardy spaces
Lipschitz spaces
Monge-Ampére singular integral operators

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abstract = "We study the Hardy spaces HFp associated with a family F of sections which is closely related to the Monge-Amp{\'e}re equation. We characterize the dual spaces of HFp, which can be realized as Carleson measure spaces, Campanato spaces, and Lipschitz spaces. Also the equivalence between the characterization of the Littlewood-Paley g-function and atomic decomposition for HFp is obtained. Then we prove that Monge-Amp{\'e}re singular operators are bounded from HFp into Lμp and bounded on both HFp and their dual spaces.",

keywords = "Campanato spaces, Carleson measure spaces, Hardy spaces, Lipschitz spaces, Monge-Amp{\'e}re singular integral operators",

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AB - We study the Hardy spaces HFp associated with a family F of sections which is closely related to the Monge-Ampére equation. We characterize the dual spaces of HFp, which can be realized as Carleson measure spaces, Campanato spaces, and Lipschitz spaces. Also the equivalence between the characterization of the Littlewood-Paley g-function and atomic decomposition for HFp is obtained. Then we prove that Monge-Ampére singular operators are bounded from HFp into Lμp and bounded on both HFp and their dual spaces.

KW - Campanato spaces

KW - Carleson measure spaces

KW - Hardy spaces

KW - Lipschitz spaces

KW - Monge-Ampére singular integral operators

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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ER -

Boundedness of Monge-Ampére singular integral operators acting on hardy spaces and their duals

Abstract

Keywords

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