The equivalence between pointwise Hardy inequalities and uniform fatness
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2009
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| _version_ | 1866915870152851456 |
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| author | Korte, Riikka Lehrbäck, Juha Tuominen, Heli |
| author_facet | Korte, Riikka Lehrbäck, Juha Tuominen, Heli |
| contents | We prove an equivalence result between the validity of a pointwise Hardy inequality in a domain and uniform capacity density of the complement. This result is new even in Euclidean spaces, but our methods apply in general metric spaces as well. We also present a new transparent proof for the fact that uniform capacity density implies the classical integral version of the Hardy inequality in the setting of metric spaces. In addition, we consider the relations between the above concepts and certain Hausdorff content conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0906_2086 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | The equivalence between pointwise Hardy inequalities and uniform fatness Korte, Riikka Lehrbäck, Juha Tuominen, Heli Analysis of PDEs 46E35, 31C45, 26D15 We prove an equivalence result between the validity of a pointwise Hardy inequality in a domain and uniform capacity density of the complement. This result is new even in Euclidean spaces, but our methods apply in general metric spaces as well. We also present a new transparent proof for the fact that uniform capacity density implies the classical integral version of the Hardy inequality in the setting of metric spaces. In addition, we consider the relations between the above concepts and certain Hausdorff content conditions. |
| title | The equivalence between pointwise Hardy inequalities and uniform fatness |
| topic | Analysis of PDEs 46E35, 31C45, 26D15 |
| url | https://arxiv.org/abs/0906.2086 |