Besov and Hölder spaces on spaces of homogeneous type

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We establish a theory of Besov spaces associated with a family of quasi-metric balls under only the doubling condition on the measure. We introduce the corresponding Hölder spaces as well, and show that the duals of some Besov spaces defined here are equivalent to the corresponding Hölder spaces. As an application, we show that Monge–Ampère singular integral operators are bounded on these spaces.

Original languageEnglish
Pages (from-to)219-263
Number of pages45
JournalStudia Mathematica
Issue number3
StatePublished - 2020


  • Besov spaces
  • Hölder spaces
  • Monge–Ampère singular integral operators


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