Besov and Hölder spaces on spaces of homogeneous type

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.