Potential theory of signed Riesz Kernels: capacity and Hausdorff measure
In this paper, we study the natural capacity γα related to the Riesz kernels x/∣x∣1 + α in ℝn, where 0 < α < n. For noninteger α, an unexpected behaviour arises: for 0 < α < 1, compact sets in ℝn with finite α-Hausdorff measure have zero γα capacity. In the Ahlfors-David regular case, fo...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2004 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/9174 |
| Acceso en línea: | https://hdl.handle.net/2445/9174 |
| Access Level: | acceso abierto |
| Palabra clave: | Teoria del potencial (Matemàtica) Geometria algebraica Potentials and capacities Hausdorff and packing measures |
| Sumario: | In this paper, we study the natural capacity γα related to the Riesz kernels x/∣x∣1 + α in ℝn, where 0 < α < n. For noninteger α, an unexpected behaviour arises: for 0 < α < 1, compact sets in ℝn with finite α-Hausdorff measure have zero γα capacity. In the Ahlfors-David regular case, for any noninteger index α, 0 < α < n, we prove that compact sets of finite α-Hausdorff measure have zero γα capacity. |
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