2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171742We give a probabilistic characterisation of the Besov-Lipschitz spaces $Lip(α,p,q)(X)$ 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 $α=\frac{d_w}{2},p=2$, $q=\infty,$ where $d_w$ is the walk dimension of the space $X.$Probability46E30; 60J35text