Rectifiability of measures and the βp coefficients
In some former works of Azzam and Tolsa it was shown that n-rectifiabilitycan be characterized in terms of a square function involving the David-Semmes β2 coecients. In the present paper we construct some counterexamples which show that a similar characterization does not hold for the βp coefficient...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:206880 |
| Acceso en línea: | https://ddd.uab.cat/record/206880 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6321904 |
| Access Level: | acceso abierto |
| Palabra clave: | Rectifiability Square functions Jones' β coefficients Corona decomposition |
| Sumario: | In some former works of Azzam and Tolsa it was shown that n-rectifiabilitycan be characterized in terms of a square function involving the David-Semmes β2 coecients. In the present paper we construct some counterexamples which show that a similar characterization does not hold for the βp coefficients with p = 2. This is in strong contrast with what happens in the case of uniform n-rectifiability. In the second part of this paper we provide an alternative argument for a recent result of Edelen, Naber, and Valtorta about the n-rectifiability of measures with bounded lower n-dimensional density. Our alternative proof follows from a slight variant of the corona decomposition in one of the aforementioned works of Azzam and Tolsa and a suitable approximation argument. |
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