Probabilistic characterisation of Besov-Lipschitz spaces on metric measure spaces
Abstract
Description
We 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 $X.$