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

Date:	2019
Abstract:	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.
Grants:	Ministerio de Ciencia e Innovación MTM-2016-77635-P Ministerio de Ciencia e Innovación MDM-2014-044
Note:	The author was supported by the ERC grant 320501 of the European Research Council (FP7/2007-2013) and partially supported by MTM-2016-77635-P, MDM-2014-044 (MICINN, Spain), 2017-SGR-395 (Catalonia), and by Marie Curie ITN MAnET (FP7-607647)
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Rectifiability ; Square functions ; Jones' β coefficients ; Corona decomposition
Published in:	Publicacions matemàtiques, Vol. 63 Núm. 2 (2019) , p. 491-519 (Articles) , ISSN 2014-4350

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

29 p, 479.8 KB

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