Boundedness of the square function and rectifiability

Svitlana Mayboroda; Alexander Volberg

doi:10.1016/j.crma.2009.07.007

Harmonic Analysis

Boundedness of the square function and rectifiability

Presented by: 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. 17-18, pp. 1051-1056.

Abstract
Résumé

Following a recent paper [X. Tolsa, Principal values for Riesz transforms and rectifiability, J. Funct. Anal. 254 (7) (2008) 1811–1863] we show that the finiteness of the square function associated with the Riesz transforms with respect to Hausdorff measure $H^{n}$ (n is an integer) on a set E, implies that E is rectifiable.

On peut modifier l'article récent [X. Tolsa, Principal values for Riesz transforms and rectifiability, J. Funct. Anal. 254 (7) (2008) 1811–1863] pour démontrer que la convergence de la fonction carrée associée aux transformations de Riesz de mesure de Hausdorff $H^{n}$ (n est un nombre entier) sur un compact E implique que E est rectifiable.

Received: 2009-04-12
Accepted: 2009-06-18
Published online: 2009-08-05

DOI: 10.1016/j.crma.2009.07.007

Author's affiliations:

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. Boundedness of the square function and rectifiability. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1051-1056. doi : 10.1016/j.crma.2009.07.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.07.007/

References
Cited by

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Cited by Sources:

^☆ The first author was partially supported by the NSF grant 0929382. The second author was partially supported by the NSF grant 0758552.

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