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

Lin, Chin-Cheng

doi:10.1090/tran/6397

Boundedness of Monge-Ampère singular integral operators acting on Hardy spaces and their duals
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Trans. Amer. Math. Soc. 368 (2016), 3075-3104 Request permission

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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