Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces

Takashi Kumagai, Nageswari Shanmugalingam, Ryosuke Shimizu

In the context of a metric measure space $(X,d,\hat{I}¼)$, we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of t…