Weak monotonicity property of Korevaar-Schoen norms on nested fractals

TL;DR

This paper investigates the weak monotonicity of Korevaar-Schoen norms related to p-energy on nested fractals, which has significant implications for analysis on fractals and metric measure spaces.

Contribution

It establishes the weak monotonicity property of Korevaar-Schoen norms on nested fractals for 1 < p < ∞, enabling new developments in fractal analysis.

Findings

Proves weak monotonicity of Korevaar-Schoen norms on nested fractals.

Facilitates construction of p-energies and Dirichlet forms on fractals.

Supports generalization of Sobolev inequalities and convergence results.

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.