Probabilistic characterisation of Besov-Lipschitz spaces on metric measure spaces

TL;DR

This paper provides a probabilistic characterization of Besov-Lipschitz spaces on metric measure spaces supporting a Markovian kernel, extending previous results to more general parameters and settings.

Contribution

It generalizes earlier characterizations of Besov-Lipschitz spaces to broader parameters and spaces with Markovian kernels, beyond specific cases.

Findings

Probabilistic characterization of Besov-Lipschitz spaces on metric measure spaces.

Extension of previous results to general parameters and spaces.

Applicable to spaces supporting a Markovian kernel with exponential bounds.

Abstract

We give a probabilistic characterisation of the Besov-Lipschitz spaces $Lip(\alpha,p,q)(X)$ on domains which support a Markovian kernel with appropriate exponential bounds. This extends former results of \cite{Jon,KPP1,KPP2,GHL} which were valid for $\alpha=\frac{d_w}{2},p=2$, $q=\infty,$ where $d_w$ is the walk dimension of the space $X.$