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Besov and Hölder spaces on spaces of homogeneous type

Volume 255 / 2020

Yongshen Han, Ming-Yi Lee, Chin-Cheng Lin Studia Mathematica 255 (2020), 219-263 MSC: Primary 42B35; Secondary 42B20. DOI: 10.4064/sm180925-17-9 Published online: 11 May 2020

Abstract

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.

Authors

  • Yongshen HanDepartment of Mathematics
    Auburn University
    Auburn, AL 36849-5310, U.S.A.
    e-mail
  • Ming-Yi LeeDepartment of Mathematics
    National Central University
    Chung-Li 320, Taiwan, Republic of China
    e-mail
  • Chin-Cheng LinDepartment of Mathematics
    National Central University
    Chung-Li 320, Taiwan, Republic of China
    e-mail

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