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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2307.10449 |
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| _version_ | 1866916081199742976 |
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| author | Cao, Shiping Chen, Zhen-Qing Kumagai, Takashi |
| author_facet | Cao, Shiping Chen, Zhen-Qing Kumagai, Takashi |
| contents | Let $(K,d)$ be a connected compact metric space and $p\in (1, \infty)$. Under the assumption of \cite[Assumption 2.15]{Ki2} and the conductive $p$-homogeneity, we show that $\mathcal{W}^p(K)\subset C(K)$ holds if and only if $p>\operatorname{dim}_{AR}(K,d)$, where $\mathcal{W}^p(K)$ is Kigami's $(1,p)$-Sobolev space and $\operatorname{dim}_{AR}(K,d)$ is the Ahlfors regular dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10449 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Kigami's conjecture of the embedding $\mathcal{W}^p(K)\subset C(K)$ Cao, Shiping Chen, Zhen-Qing Kumagai, Takashi Functional Analysis 31E05 Let $(K,d)$ be a connected compact metric space and $p\in (1, \infty)$. Under the assumption of \cite[Assumption 2.15]{Ki2} and the conductive $p$-homogeneity, we show that $\mathcal{W}^p(K)\subset C(K)$ holds if and only if $p>\operatorname{dim}_{AR}(K,d)$, where $\mathcal{W}^p(K)$ is Kigami's $(1,p)$-Sobolev space and $\operatorname{dim}_{AR}(K,d)$ is the Ahlfors regular dimension. |
| title | On Kigami's conjecture of the embedding $\mathcal{W}^p(K)\subset C(K)$ |
| topic | Functional Analysis 31E05 |
| url | https://arxiv.org/abs/2307.10449 |