Boundedness of Monge-Ampére singular integral operators acting on hardy spaces and their duals

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Abstract

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.

Original languageEnglish
Pages (from-to)3075-3104
Number of pages30
JournalTransactions of the American Mathematical Society
Volume368
Issue number5
DOIs
StatePublished - May 2016

Keywords

  • Campanato spaces
  • Carleson measure spaces
  • Hardy spaces
  • Lipschitz spaces
  • Monge-Ampére singular integral operators

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