$L^p$-Poincar\'e inequalities on nested fractals
Functional Analysis
2023-06-29 v4 Analysis of PDEs
Metric Geometry
Probability
Abstract
We prove on some nested fractals scale invariant -Poincar\'e inequalities on metric balls in the range . Our proof is based on the development of the local -theory of Korevaar-Schoen-Sobolev spaces on fractals using heat kernel methods. Applications to scale invariant Sobolev inequalities and to the study of maximal functions and Haj\l{}asz-Sobolev spaces on fractals are given. Results are illustrated and further developed in the case of the Vicsek set.
Cite
@article{arxiv.2012.03090,
title = {$L^p$-Poincar\'e inequalities on nested fractals},
author = {Fabrice Baudoin and Li Chen},
journal= {arXiv preprint arXiv:2012.03090},
year = {2023}
}
Comments
Paper is outdated in terms of scope and methods. Also requires several revisions. See in particular 2207.02949