报告摘要：
| We study the Hardy spaces $H^p_{Cal F}$ associated with a family $Cal F$ of sections which is closely related to the Monge-Amp`ere equation. We characterize the dual spaces of $H^p_{Cal F}$, which can be realized as Carleson measure spaces, Campanato spaces, and Lipschitz spaces. Then we prove that Monge-Amp`ere singular operators are bounded on both $H^p_{Cal F}$ and their dual spaces.
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