Characterization of Campanato spaces associated with parabolic sections

Ming Yi Lee; Chin Cheng Lin; Xinfeng Wu

doi:10.4310/AJM.2016.v20.n1.a8

Characterization of Campanato spaces associated with parabolic sections

Ming Yi Lee, Chin Cheng Lin, Xinfeng Wu

Department of Mathematics

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

2 Scopus citations

Abstract

We study the Campanato spaces Λ^k _q,P associated with a family P of parabolic sections which are closely related to the parabolic Monge-Ampère equation. We characterize these spaces in terms of Lipschitz spaces Li_P^α P. We also introduce the corresponding Hardy spaces H^p _P and demonstrate the equivalence between the Littlewood-Paley g-functions and atomic decompositions for elements in H^p _P. Moreover, we show that Campanato spaces are the duals of Hardy spaces.

Original language	English
Pages (from-to)	183-198
Number of pages	16
Journal	Asian Journal of Mathematics
Volume	20
Issue number	1
DOIs	https://doi.org/10.4310/AJM.2016.v20.n1.a8
State	Published - 2016

Keywords

Campanato spaces
Hardy spaces
Lipschitz spaces
Monge-Ampère equations
Parabolic sections

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10.4310/AJM.2016.v20.n1.a8

Besov Spaces Associated to Monge-Ampere Equations(1/2)
Lee, M.-Y. (PI)
1/08/15 → 31/07/16
Project: Research

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title = "Characterization of Campanato spaces associated with parabolic sections",

abstract = "We study the Campanato spaces Λk q,P associated with a family P of parabolic sections which are closely related to the parabolic Monge-Amp{\`e}re equation. We characterize these spaces in terms of Lipschitz spaces LiPα P. We also introduce the corresponding Hardy spaces Hp P and demonstrate the equivalence between the Littlewood-Paley g-functions and atomic decompositions for elements in Hp P. Moreover, we show that Campanato spaces are the duals of Hardy spaces.",

keywords = "Campanato spaces, Hardy spaces, Lipschitz spaces, Monge-Amp{\`e}re equations, Parabolic sections",

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AU - Wu, Xinfeng

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N2 - We study the Campanato spaces Λk q,P associated with a family P of parabolic sections which are closely related to the parabolic Monge-Ampère equation. We characterize these spaces in terms of Lipschitz spaces LiPα P. We also introduce the corresponding Hardy spaces Hp P and demonstrate the equivalence between the Littlewood-Paley g-functions and atomic decompositions for elements in Hp P. Moreover, we show that Campanato spaces are the duals of Hardy spaces.

AB - We study the Campanato spaces Λk q,P associated with a family P of parabolic sections which are closely related to the parabolic Monge-Ampère equation. We characterize these spaces in terms of Lipschitz spaces LiPα P. We also introduce the corresponding Hardy spaces Hp P and demonstrate the equivalence between the Littlewood-Paley g-functions and atomic decompositions for elements in Hp P. Moreover, we show that Campanato spaces are the duals of Hardy spaces.

KW - Campanato spaces

KW - Hardy spaces

KW - Lipschitz spaces

KW - Monge-Ampère equations

KW - Parabolic sections

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VL - 20

SP - 183

EP - 198

JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

IS - 1

ER -

Characterization of Campanato spaces associated with parabolic sections

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Keywords

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Besov Spaces Associated to Monge-Ampere Equations(1/2)

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