Boundedness of Monge-Ampère singular integral operators acting on Hardy spaces and their duals
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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.References
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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
- Received by editor(s): September 7, 2013
- Received by editor(s) in revised form: February 7, 2014
- Published electronically: August 19, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 3075-3104
- MSC (2010): Primary 42B20, 42B30; Secondary 42B35
- DOI: https://doi.org/10.1090/tran/6397
- MathSciNet review: 3451870