Equivalence of Besov spaces on p.c.f. self-similar sets
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866910704412393472 |
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| author | Cao, Shiping Qiu, Hua |
| author_facet | Cao, Shiping Qiu, Hua |
| contents | On p.c.f. self-similar sets, of which the walk dimensions of heat kernels are in general larger than 2, we find a sharp region where two classes of Besov spaces, the heat Besov spaces $B^{p,q}_σ(K)$ and the Lipschitz-Besov spaces $Λ^{p,q}_σ(K)$, are identitical. In particular, we provide concrete examples that $B^{p,q}_σ(K)=Λ^{p,q}_σ(K)$ with $σ>1$. Our method is purely analytical, and does not involve any heat kernel estimate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2003_03706 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Equivalence of Besov spaces on p.c.f. self-similar sets Cao, Shiping Qiu, Hua Functional Analysis Analysis of PDEs 28A80 On p.c.f. self-similar sets, of which the walk dimensions of heat kernels are in general larger than 2, we find a sharp region where two classes of Besov spaces, the heat Besov spaces $B^{p,q}_σ(K)$ and the Lipschitz-Besov spaces $Λ^{p,q}_σ(K)$, are identitical. In particular, we provide concrete examples that $B^{p,q}_σ(K)=Λ^{p,q}_σ(K)$ with $σ>1$. Our method is purely analytical, and does not involve any heat kernel estimate. |
| title | Equivalence of Besov spaces on p.c.f. self-similar sets |
| topic | Functional Analysis Analysis of PDEs 28A80 |
| url | https://arxiv.org/abs/2003.03706 |