Boundary Value Problems
Volume 2010 (2010), Article ID 513186, 9 pages
doi:10.1155/2010/513186
Research Article

Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains

Ricardo Abreu-Blaya,1 Juan Bory-Reyes,2 and Paul Bosch3

1Departamento de Matemática, Universidad de Holguín, Holguín 80100, Cuba
2Departamento de Matemática, Universidad de Oriente, Santiago de Cuba 90500, Cuba
3Facultad de Ingeniería, Universidad Diego Portales, Santiago de Chile 8370179, Chile

Received 1 December 2009; Accepted 20 March 2010

Academic Editor: Gary Lieberman

Copyright © 2010 Ricardo Abreu-Blaya et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Monogenic extension theorem of complex Clifford algebras-valued functions over a bounded domain with fractal boundary is obtained. The paper is dealing with the class of Hölder continuous functions. Applications to holomorphic functions theory of several complex variables as well as to that of the so-called biregular functions will be deduced directly from the isotonic approach.