Uniform rectifiability and harmonic measure, II: Poisson kernels in Lp imply uniform rectifiability
We present the converse to a higher-dimensional, scale-invariant version of the classical F. and M. Riesz theorem, proved by the first two authors. More precisely, for n ≥ 2, for an Ahlfors-David regular domain Ω ⊂ ℝn+1 which satisfies the Harnack chain condition plus an interior (but not exterior)...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/197716 |
| Acceso en línea: | http://hdl.handle.net/10261/197716 |
| Access Level: | acceso abierto |
| Palabra clave: | Aoo Muckenhoupt weights Carleson measures Poisson kernel Uniform rectifiability Harmonic measure |
| Sumario: | We present the converse to a higher-dimensional, scale-invariant version of the classical F. and M. Riesz theorem, proved by the first two authors. More precisely, for n ≥ 2, for an Ahlfors-David regular domain Ω ⊂ ℝn+1 which satisfies the Harnack chain condition plus an interior (but not exterior) corkscrew condition, we show that absolute continuity of the harmonic measure with respect to the surface measure on ∂Ω, with scale-invariant higher integrability of the Poisson kernel, is sufficient to imply quantitative rectifiability of ∂Ω. |
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