Heat semigroup and BV functions

In abstract Dirichlet spaces, we present  a theory of Besov spaces which is based on the heat semigroup. This approach offers a new perspective on the class of bounded variation functions in settings including Riemannian manifolds, sub-Riemannian manifolds. In rough spaces like fractals it offers totally new research directions. The key assumption on the underlying space is a weak Bakry-Emery type curvature assumption.

The talk is based on joint works with Patricia Alonso-Ruiz, Li Chen, Luke Rogers, Nageswari Shanmugalingam and Alexander Teplyaev.