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Rectifiability of measures and the βp coefficients
Tolsa Domènech, Xavier (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Fecha: 2019
Resumen: 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.
Derechos: Tots els drets reservats
Lengua: Anglès.
Documento: article ; recerca ; publishedVersion
Materia: Rectifiability ; Square functions ; Jones' β coefficients ; Corona decomposition
Publicado en: Publicacions matemàtiques, Vol. 63 Núm. 2 (2019) , p. 491-519 (Articles) , ISSN 2014-4350

Adreça original: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/358950
DOI: 10.5565/PUBLMAT6321904


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