Sharp capacity estimates in s-John domains
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arXiv
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| Format: | Preprint |
| Published: |
2014
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| _version_ | 1866910646492200960 |
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| author | Guo, Chang-Yu |
| author_facet | Guo, Chang-Yu |
| contents | It is well-known that several problems related to analysis on $s$-John domains can be unified by certain capacity lower estimates. In this paper, we obtain general lower bounds of $p$-capacity of a compact set $E$ and the central Whitney cube $Q_0$ in terms of the Hausdorff $q$-content of $E$ in an $s$-John domain $Ω$. Moreover, we construct several examples to show the essential sharpness of our estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1412_2468 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Sharp capacity estimates in s-John domains Guo, Chang-Yu Complex Variables 30C65, 46E35 It is well-known that several problems related to analysis on $s$-John domains can be unified by certain capacity lower estimates. In this paper, we obtain general lower bounds of $p$-capacity of a compact set $E$ and the central Whitney cube $Q_0$ in terms of the Hausdorff $q$-content of $E$ in an $s$-John domain $Ω$. Moreover, we construct several examples to show the essential sharpness of our estimates. |
| title | Sharp capacity estimates in s-John domains |
| topic | Complex Variables 30C65, 46E35 |
| url | https://arxiv.org/abs/1412.2468 |