no. 17-18
Harmonic Analysis
Boundedness of the square function and rectifiability
[Une fonction carrée de la transformation de Riesz et rectifiabilité]

Présenté par : Gilles Pisier

Mayboroda, Svitlana1 ; Volberg, Alexander2
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, Tome 347 (2009) no. 17-18, pp. 1051-1056.

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 Hn (n est un nombre entier) sur un compact E implique que E est rectifiable.

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 Hn (n is an integer) on a set E, implies that E is rectifiable.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.07.007
Mayboroda, Svitlana 1 ; Volberg, Alexander 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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Mayboroda, Svitlana; Volberg, Alexander. Boundedness of the square function and rectifiability. Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 1051-1056. doi : 10.1016/j.crma.2009.07.007. http://www.numdam.org/articles/10.1016/j.crma.2009.07.007/

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Cité par Sources :

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