On the Domains of Dirichlet Forms on Metric Measure Spaces

TL;DR

This paper investigates the relationship between local and non-local Dirichlet forms on metric measure spaces, establishing strict inclusion of their domains under general conditions.

Contribution

It provides a theoretical comparison showing the domain of local Dirichlet forms is strictly smaller than that of stable-like non-local forms on general metric measure spaces.

Findings

The domain of local Dirichlet forms is strictly contained in that of non-local forms.

The result applies to general metric measure spaces.

Clarifies the structural differences between local and non-local Dirichlet forms.

Abstract

We prove that the domain of the local Dirichlet form is strictly contained in the domain of any stable-like non-local Dirichlet form on general metric measure spaces.