Rademachertype Theorems and SobolevtoLipschitz Properties for Strongly Local Dirichlet Spaces
Abstract
We extensively discuss the Rademacher and SobolevtoLipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many nonsmooth and infinitedimensional examples. As an application, we prove the integral Varadhan shorttime asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 DOI:
 10.48550/arXiv.2008.01492
 arXiv:
 arXiv:2008.01492
 Bibcode:
 2020arXiv200801492D
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Metric Geometry;
 Mathematics  Probability;
 31C25 (Primary) 30L99;
 31E05 (Secondary)
 EPrint:
 44 pages, list of notations (end), Title, Abstract and Introduction have been changed. Lemma 2.10, Corollary 2.35, and Proposition 3.31 have been removed. Proposition 3.7 and Corollary 4.17 have been added