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arXiv · 2012.03090

$L^p$-Poincar\'e inequalities on nested fractals

Fabrice Baudoin·Li Chen
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Abstract

We prove on some nested fractals scale invariant $L^p$-Poincar\'e inequalities on metric balls in the range $1 \le p \le 2$. Our proof is based on the development of the local $L^p$-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.

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BibTeXRIS

Fabrice Baudoin, Li Chen. 2020-12-05. $L^p$-Poincar\'e inequalities on nested fractals. https://arxiv.org/abs/2012.03090

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