Besov and Hölder spaces on spaces of homogeneous type
Volume 255 / 2020
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.
