Korevaar-Schoen \(p\)-energy forms and associated \(p\)-energy measures on fractals

We construct good \(p\)-energy forms on metric measure spaces as pointwise subsequential limits of Besov-type \(p\)-energy functionals under certain geometric/analytic conditions. Such forms are often called Korevaar-Schoen \(p\)-energy forms in the literature. As an advantage of our approach, the a...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Kajino, Naotaka, Shimizu, Ryosuke
Format: Article
Language:English
Subjects:
Self-similarity
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Summary:We construct good \(p\)-energy forms on metric measure spaces as pointwise subsequential limits of Besov-type \(p\)-energy functionals under certain geometric/analytic conditions. Such forms are often called Korevaar-Schoen \(p\)-energy forms in the literature. As an advantage of our approach, the associated \(p\)-energy measures are obtained and investigated. We also prove that our construction is applicable to the settings of Kigami [Mem. Eur. Math. Soc. 5 (2023)] and Cao-Gu-Qiu [Adv. Math. 405 (2022), no. 108517], yields Korevaar-Schoen \(p\)-energy forms comparable to the \(p\)-energy forms constructed in these papers, and can be further modified in the case of self-similar sets to obtain self-similar \(p\)-energy forms keeping most of the good properties of Korevaar-Schoen ones.
ISSN:2331-8422