The Plemelj-Privalov theorem in Clifford analysis

This Note gives geometric conditions on a surface of R-n so that the Hilbert transform oil that surface in the framework of Clifford analysis defines a bounded operator in the Holder Continuous functions classes. This result provides a generalization of the well-known theorem of Plemelj and Privalov for curves in R-2. To cite this article: R. Abreu Blaya et al., C R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.