Comptes Rendus
no. 5-6
Complex Analysis
The Plemelj–Privalov theorem in Clifford analysis
[Le theorème de Plemelj–Privalov au domaine de l'analyse de Clifford]

Présenté par : Jean-Pierre Demailly

Ricardo Abreu Blaya1 ; Juan Bory Reyes2 ; Tania Moreno García1
1 Facultad de Informática y Matemática, Universidad de Holguín, Holguín 80100, Cuba
2 Departamento de Matemática, Universidad de Oriente, Santiago de Cuba 90500, Cuba
Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 223-226.

Cette Note propose une condition géométrique sur une surface de Rn de façon que la transformée de Hilbert sur cette surface, dans le contexte de l'analyse de Clifford, définisse un opérateur borné dans les classes de fonctions de Hölder. Cet résultat généralise le théorème bien connu de Plemelj et Privalov pour des courbes de R2.

This Note gives geometric conditions on a surface of Rn so that the Hilbert transform on that surface in the framework of Clifford analysis defines a bounded operator in the Hölder continuous functions classes. This result provides a generalization of the well-known theorem of Plemelj and Privalov for curves in R2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.01.029

Ricardo Abreu Blaya 1 ; Juan Bory Reyes 2 ; Tania Moreno García 1

1 Facultad de Informática y Matemática, Universidad de Holguín, Holguín 80100, Cuba
2 Departamento de Matemática, Universidad de Oriente, Santiago de Cuba 90500, Cuba 
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Ricardo Abreu Blaya; Juan Bory Reyes; Tania Moreno García. The Plemelj–Privalov theorem in Clifford analysis. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 223-226. doi : 10.1016/j.crma.2009.01.029. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.01.029/

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