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Boundedness of Monge-Ampère singular integral operators acting on Hardy spaces and their duals


Author: Chin-Cheng Lin
Journal: Trans. Amer. Math. Soc. 368 (2016), 3075-3104
MSC (2010): Primary 42B20, 42B30; Secondary 42B35
DOI: https://doi.org/10.1090/tran/6397
Published electronically: August 19, 2015
MathSciNet review: 3451870
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Abstract: We study the Hardy spaces $ H^p_{\mathcal {F}}$ associated with a family $ \mathcal {F}$ of sections which is closely related to the Monge-Ampère equation. We characterize the dual spaces of $ H^p_{\mathcal {F}}$, 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^p_{\mathcal {F}}$ is obtained. Then we prove that Monge-Ampère singular operators are bounded from $ H^p_{\mathcal {F}}$ into $ L^p_\mu $ and bounded on both $ H^p_{\mathcal {F}}$ and their dual spaces.


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Additional Information

Chin-Cheng Lin
Affiliation: Department of Mathematics, National Central University, Chung-Li, Taiwan 320, Republic of China
Email: clin@math.ncu.edu.tw

DOI: https://doi.org/10.1090/tran/6397
Keywords: Campanato spaces, Carleson measure spaces, Hardy spaces, Lipschitz spaces, Monge-Amp\`ere singular integral operators
Received by editor(s): September 7, 2013
Received by editor(s) in revised form: February 7, 2014
Published electronically: August 19, 2015
Article copyright: © Copyright 2015 American Mathematical Society