This Note gives geometric conditions on a surface of 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 .
Cette Note propose une condition géométrique sur une surface de 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 .
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@article{CRMATH_2009__347_5-6_223_0,
author = {Abreu Blaya, Ricardo and Bory Reyes, Juan and Moreno Garc{\'\i}a, Tania},
title = {The {Plemelj{\textendash}Privalov} theorem in {Clifford} analysis},
journal = {Comptes Rendus. Math\'ematique},
pages = {223--226},
publisher = {Elsevier},
volume = {347},
number = {5-6},
year = {2009},
doi = {10.1016/j.crma.2009.01.029},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.01.029/}
}
TY - JOUR AU - Abreu Blaya, Ricardo AU - Bory Reyes, Juan AU - Moreno García, Tania TI - The Plemelj–Privalov theorem in Clifford analysis JO - Comptes Rendus. Mathématique PY - 2009 SP - 223 EP - 226 VL - 347 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.01.029/ DO - 10.1016/j.crma.2009.01.029 LA - en ID - CRMATH_2009__347_5-6_223_0 ER -
%0 Journal Article %A Abreu Blaya, Ricardo %A Bory Reyes, Juan %A Moreno García, Tania %T The Plemelj–Privalov theorem in Clifford analysis %J Comptes Rendus. Mathématique %D 2009 %P 223-226 %V 347 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.01.029/ %R 10.1016/j.crma.2009.01.029 %G en %F CRMATH_2009__347_5-6_223_0
Abreu Blaya, Ricardo; Bory Reyes, Juan; Moreno García, Tania. 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. http://www.numdam.org/articles/10.1016/j.crma.2009.01.029/
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