The weak-A∞ property of harmonic and ρ-harmonic measures implies uniform rectifiability
Let E ⊂ R, n ≥ 2, be an Ahlfors-David regular set of dimension n. We show that the weak-A property of harmonic measure, for the open set ω:= R \ E, implies uniform rectifiability of E. More generally, we establish a similar result for the Riesz measure, ρ-harmonic measure, associated to the ρ-Laplac...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:dnet:digitalcsic_::e03b9bd868272a87d198709149a9a9c0 |
| Acceso en línea: | http://hdl.handle.net/10261/199107 |
| Access Level: | acceso abierto |
| Palabra clave: | Harmonic measure and p-harmonic measure Poisson kernel Uniform rectifiability Carleson measures Green function Weak-A1 |
| Sumario: | Let E ⊂ R, n ≥ 2, be an Ahlfors-David regular set of dimension n. We show that the weak-A property of harmonic measure, for the open set ω:= R \ E, implies uniform rectifiability of E. More generally, we establish a similar result for the Riesz measure, ρ-harmonic measure, associated to the ρ-Laplace operator, 1 < ρ < ∞. |
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