$L^p$-Poincaré inequalities on nested fractals

Document Type

Article

Publication Date

12-5-2020

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 kernels methods. Applications to scale invariant Sobolev inequalities and to the study of maximal functions and Haj\l{}asz-Sobolev spaces on fractals are given.

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