Weak monotonicity property of Korevaar-Schoen norms on nested fractals

Abstract

In this paper, we study the weak monotonicity property of p-energy related Korevaar-Schoen norms on connected nested fractals for $1<p<\infty$. Such property has many important applications on fractals and other metric measure spaces, such as constructing p-energies (when $p=2$ this is basically a Dirichlet form), generalizing the classical Sobolev type inequalities and the celebrated Bourgain-Brezis-Mironescu convergence.

10 pages,1 figure