Finite square function implies integer dimension

Svitlana Mayboroda; Alexander Volberg

doi:10.1016/j.crma.2009.09.020

Harmonic Analysis/Functional Analysis

Finite square function implies integer dimension
[Pour que la fonction carrée de mesure de Hausdorff soit finie il faut que la dimension de mesure soit entier]

Présenté par : Gilles Pisier

Svitlana Mayboroda ¹ ; Alexander Volberg ²

¹ Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, USA
² Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1271-1276.

Résumé
Abstract

On peut modifier l'article recent (Tolsa and Ruiz de Villa, 2008) pour démontrer que la convergence de la fonction carrée associée aux transformations de Riesz de mesure de Hausdorff $H^{s}$ implique que s est un nombre entier.

Following a recent paper (Tolsa and Ruiz de Villa, 2008) we show that the finiteness of square function associated with the Riesz transforms with respect to Hausdorff measure $H^{s}$ implies that s is integer.

Reçu le : 2009-05-02
Accepté le : 2009-09-21
Publié le : 2009-10-21

DOI : 10.1016/j.crma.2009.09.020

Affiliations des auteurs :

Svitlana Mayboroda ¹ ; Alexander Volberg ²

¹ Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, USA
² Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

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Svitlana Mayboroda; Alexander Volberg. Finite square function implies integer dimension. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1271-1276. doi : 10.1016/j.crma.2009.09.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.020/

Bibliographie
Cité par

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Benjamin Jaye; Fedor Nazarov; Xavier Tolsa The measures with an associated square function operator bounded in $L^{2}$ , Advances in Mathematics, Volume 339 (2018), pp. 60-112 | DOI:10.1016/j.aim.2018.09.025 | Zbl:1483.42012
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Александр Львович Вольберг; Alexander L'vovich Vol'berg; Владимир Яковлевич Эйдерман; Vladimir Yakovlevich Eiderman Неоднородный гармонический анализ: 16 лет развития, Успехи математических наук, Volume 68 (2013) no. 6(414), p. 3 | DOI:10.4213/rm9556
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Svitlana Mayboroda; Alexander Volberg Boundedness of the square function and rectifiability, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 347 (2009) no. 17-18, pp. 1051-1056 | DOI:10.1016/j.crma.2009.07.007 | Zbl:1185.28009

Cité par 6 documents. Sources : Crossref, zbMATH

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