Characterization of Campanato spaces associated with parabolic sections

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We study the Campanato spaces Λk q,P associated with a family P of parabolic sections which are closely related to the parabolic Monge-Ampère equation. We characterize these spaces in terms of Lipschitz spaces LiPα P. We also introduce the corresponding Hardy spaces Hp P and demonstrate the equivalence between the Littlewood-Paley g-functions and atomic decompositions for elements in Hp P. Moreover, we show that Campanato spaces are the duals of Hardy spaces.

Original languageEnglish
Pages (from-to)183-198
Number of pages16
JournalAsian Journal of Mathematics
Issue number1
StatePublished - 2016


  • Campanato spaces
  • Hardy spaces
  • Lipschitz spaces
  • Monge-Ampère equations
  • Parabolic sections


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