We study the Hardy spaces HFp associated with a family F of sections which is closely related to the Monge-Ampére equation. We characterize the dual spaces of HFp, 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 HFp is obtained. Then we prove that Monge-Ampére singular operators are bounded from HFp into Lμp and bounded on both HFp and their dual spaces.
|頁（從 - 到）||3075-3104|
|期刊||Transactions of the American Mathematical Society|
|出版狀態||已出版 - 5月 2016|