no. 21-22
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

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. 21-22, pp. 1271-1276.

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 Hs 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 Hs implies that s is integer.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.09.020
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. Finite square function implies integer dimension. Comptes Rendus. Mathématique, Tome 347 (2009) no. 21-22, pp. 1271-1276. doi : 10.1016/j.crma.2009.09.020. http://www.numdam.org/articles/10.1016/j.crma.2009.09.020/

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