Korevaar-Schoen $p$-energy forms and associated $p$-energy measures on fractals
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866914959439429632 |
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| author | Kajino, Naotaka Shimizu, Ryosuke |
| author_facet | Kajino, Naotaka Shimizu, Ryosuke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Korevaar-Schoen $p$-energy forms and associated $p$-energy measures on fractals Kajino, Naotaka Shimizu, Ryosuke Functional Analysis Metric Geometry 28A80, 46E36, 39B62 (Primary) 31C25, 31C45, 31E05 (Secondary) 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. |
| title | Korevaar-Schoen $p$-energy forms and associated $p$-energy measures on fractals |
| topic | Functional Analysis Metric Geometry 28A80, 46E36, 39B62 (Primary) 31C25, 31C45, 31E05 (Secondary) |
| url | https://arxiv.org/abs/2404.13435 |