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Pointwise characterization of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type

Volume 268 / 2023

Ryan Alvarado, Fan Wang, Dachun Yang, Wen Yuan Studia Mathematica 268 (2023), 121-166 MSC: Primary 46E36; Secondary 46E35, 42B25, 30L99. DOI: 10.4064/sm210621-29-4 Published online: 28 July 2022

Abstract

The authors establish a pointwise characterization of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type via clarifying the relation between Hajłasz–Sobolev spaces, Hajłasz–Besov and Hajłasz–Triebel–Lizorkin spaces, grand Besov and Triebel–Lizorkin spaces, and Besov and Triebel–Lizorkin spaces. A major novelty of this article is that all results presented get rid of both the dependence on the reverse doubling condition of the measure and the metric condition of the quasi-metric under consideration. Moreover, the pointwise characterization of the inhomogeneous version is new even when the underlying space is an RD-space.

Authors

  • Ryan AlvaradoDepartment of Mathematics and Statistics
    Amherst College
    303 Seeley Mudd
    Amherst, MA 01002, USA
    e-mail
  • Fan WangLaboratory of Mathematics and Complex Systems
    (Ministry of Education of China)
    School of Mathematical Sciences
    Beijing Normal University
    Beijing 100875, People’s Republic of China
    e-mail
  • Dachun YangLaboratory of Mathematics and Complex Systems
    (Ministry of Education of China)
    School of Mathematical Sciences
    Beijing Normal University
    Beijing 100875, People’s Republic of China
    e-mail
  • Wen YuanLaboratory of Mathematics and Complex Systems
    (Ministry of Education of China)
    School of Mathematical Sciences
    Beijing Normal University
    Beijing 100875, People’s Republic of China
    e-mail

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