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arXiv · 2603.00659

The Hölder regularity of harmonic function on bounded and unbounded p.c.f self-similar sets

Jin Gao·Yijun Song
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Abstract

In this paper, we prove a generalized reverse Hölder inequality of harmonic functions on cable systems induced by post-critically finite (p.c.f.) self-similar sets. Furthermore, we also establish the Hölder regularity of harmonic functions on both bounded and unbounded p.c.f. self-similar sets, which does not involve heat kernel estimates and resistance estimates.

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Jin Gao, Yijun Song. 2026-03-05. The Hölder regularity of harmonic function on bounded and unbounded p.c.f self-similar sets. https://arxiv.org/abs/2603.00659

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