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arXiv · 2112.10932

$p$-energies on p.c.f. self-similar sets

Shiping Cao·Qingsong Gu·Hua Qiu
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Abstract

We study $p$-energies on post critically finite (p.c.f.) self-similar sets for $1<p<\infty$, as limits of discrete $p$-energies on approximation graphs, extending the construction of Dirichlet forms, the $p=2$ setting. By suitably enlarging the choices of discrete $p$-energies, and employing the energy averaging method developed by Kusuoka-Zhou, we prove the existence of symmetric $p$-energies on affine nested fractals, and extend Sabot's celebrated criterion for existence and non-existence of Dirichlet forms on p.c.f. self-similar sets to the $1<p<\infty$ setting.

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BibTeXRIS

Shiping Cao, Qingsong Gu, Hua Qiu. 2021-12-21. $p$-energies on p.c.f. self-similar sets. https://arxiv.org/abs/2112.10932

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