Pointwise characterization of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type
Tom 268 / 2023
Studia Mathematica 268 (2023), 121-166
MSC: Primary 46E36; Secondary 46E35, 42B25, 30L99.
DOI: 10.4064/sm210621-29-4
Opublikowany online: 28 July 2022
Streszczenie
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.
