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2005 Hardy spaces associated to the sections
Yong Ding, Chin-Cheng Lin
Tohoku Math. J. (2) 57(2): 147-170 (2005). DOI: 10.2748/tmj/1119888333

Abstract

In this paper we define the Hardy space $H^1_{\Cal F}(\Bbb R^n)$ associated with a family $\Cal {F}$ of sections and a doubling measure $\mu$, where $\Cal {F}$ is closely related to the Monge-Ampère equation. Furthermore, we show that the dual space of $H^1_{\Cal F}(\Bbb R^n)$ is just the space $B\!M\!O_{\Cal F}(\Bbb R^n)$, which was first defined by Caffarelli and Gutiérrez. We also prove that the Monge-Ampère singular integral operator is bounded from $H^1_{\Cal F}(\Bbb R^n)$ to $L^1(\Bbb R^n,d\mu)$.

Citation

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Yong Ding. Chin-Cheng Lin. "Hardy spaces associated to the sections." Tohoku Math. J. (2) 57 (2) 147 - 170, 2005. https://doi.org/10.2748/tmj/1119888333

Information

Published: 2005
First available in Project Euclid: 27 June 2005

zbMATH: 1085.42014
MathSciNet: MR2137464
Digital Object Identifier: 10.2748/tmj/1119888333

Subjects:
Primary: 42B30
Secondary: 35B45

Rights: Copyright © 2005 Tohoku University

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Vol.57 • No. 2 • 2005
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