English

Metrics on the Sierpinski carpet by weight functions

Functional Analysis 2018-06-15 v2

Abstract

We construct certain metrics on the Sierpinski carpet via a class of self-similar weight functions. Using these metrics and by applying known results, we obtain the two-sided sub-Gaussian heat kernel estimates of time change of the standard diffusion on the Sierpinski carpet with respect to self-similar measures. This proves a conjecture by Kigami.

Keywords

Cite

@article{arxiv.1806.02947,
  title  = {Metrics on the Sierpinski carpet by weight functions},
  author = {Qingsong Gu and Hua Qiu and Huo-Jun Ruan},
  journal= {arXiv preprint arXiv:1806.02947},
  year   = {2018}
}

Comments

21 pages, 4 figures