Comptes Rendus
no. 10
Mathematical analysis/Functional analysis
Dimension of gradient measures

Presented by: Gilles Pisier

Dmitriy M. Stolyarov1, 2; Michal Wojciechowski3
1 St. Petersburg Department of Steklov Mathematical Institute RAS, Fontanka 27, St. Petersburg, Russia
2 Chebyshev Laboratory (SPbU), 14th Line 29B, Vasilyevsky Island, St. Petersburg, Russia
3 Institute of Mathematics, Polish Academy of Sciences, 00-956 Warszawa, Poland
Comptes Rendus. Mathématique, Volume 352 (2014) no. 10, pp. 791-795.

We prove that if pure derivatives of a function on Rn are complex measures, then their lower Hausdorff dimension is at least n−1. The derivatives with respect to different coordinates may be of different order.

Supposons que les dérivées pures (pas nécéssairement du même ordre) d'une fonction sur Rn soient des mesures de Radon finies. On montre que leur dimension inférieure de Hausdorf est alors au moins n−1.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.08.011

Dmitriy M. Stolyarov 1, 2; Michal Wojciechowski 3

1 St. Petersburg Department of Steklov Mathematical Institute RAS, Fontanka 27, St. Petersburg, Russia
2 Chebyshev Laboratory (SPbU), 14th Line 29B, Vasilyevsky Island, St. Petersburg, Russia
3 Institute of Mathematics, Polish Academy of Sciences, 00-956 Warszawa, Poland 
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Dmitriy M. Stolyarov; Michal Wojciechowski. Dimension of gradient measures. Comptes Rendus. Mathématique, Volume 352 (2014) no. 10, pp. 791-795. doi : 10.1016/j.crma.2014.08.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.08.011/

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