Rademacher-type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces

TL;DR

This paper explores Rademacher and Sobolev-to-Lipschitz properties in strongly local Dirichlet spaces, providing new examples and applying results to short-time asymptotics of Dirichlet forms.

Contribution

It extends the understanding of these properties to non-smooth and infinite-dimensional spaces without relying on square field operators.

Findings

Established Rademacher and Sobolev-to-Lipschitz properties in new settings

Provided numerous non-smooth and infinite-dimensional examples

Proved Varadhan short-time asymptotic results for a broad class of Dirichlet forms

Abstract

We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms.