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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  • Yufeng Wang; Zhongxiang Zhang H-B theorems of Cauchy integral operators in Clifford analysis, Advances in Applied Clifford Algebras, Volume 35 (2025) no. 1, p. 19 (Id/No 10) | DOI:10.1007/s00006-025-01371-0 | Zbl:7978192
  • José Luis Serrano Ricardo; Juan Bory Reyes; Ricardo Abreu Blaya Singular integral operators and a ∂―-problem for (φ,ψ)-harmonic functions, Analysis and Mathematical Physics, Volume 11 (2021) no. 4, p. 26 (Id/No 155) | DOI:10.1007/s13324-021-00590-5 | Zbl:1476.30162
  • Juan Bory Reyes; Ricardo Abreu Blaya; Ramón Martin Rodríguez Dagnino; Boris Aleksandrovich Kats On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation, Analysis and Mathematical Physics, Volume 9 (2019) no. 1, pp. 483-496 | DOI:10.1007/s13324-018-0210-3 | Zbl:1418.30045
  • Lianet De la Cruz Toranzo; Ricardo Abreu Blaya; Juan Bory Reyes On the Plemelj-Privalov theorem in Clifford analysis involving higher order Lipschitz classes, Journal of Mathematical Analysis and Applications, Volume 480 (2019) no. 2, p. 13 (Id/No 123411) | DOI:10.1016/j.jmaa.2019.123411 | Zbl:1427.30074
  • Lianet De la Cruz Toranzo; Arsenio Moreno García; Tania Moreno García; Ricardo Abreu Blaya; Juan Bory Reyes A bimonogenic Cauchy transform on higher order Lipschitz classes, Mediterranean Journal of Mathematics, Volume 16 (2019) no. 1, p. 14 (Id/No 13) | DOI:10.1007/s00009-018-1280-z | Zbl:1412.30137
  • Ricardo Abreu-Blaya; Juan Bory-Reyes Hölder norm estimate for the Hilbert transform in Clifford analysis, Bulletin of the Brazilian Mathematical Society. New Series, Volume 41 (2010) no. 3, pp. 389-398 | DOI:10.1007/s00574-010-0017-9 | Zbl:1222.30040

Cité par 6 documents. Sources : zbMATH

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