Resumen
We study the analogue of the Cauchy transform for the theory of solutions of the Hodge/de Rham system in the case of a rectifiable surface of integration which additionally satisfies an Ahlfors/David regularity condition and we prove the Cauchy integral formula, the Plemelj/Privalov theorem and the Sokhotski/Plemelj theorem for it, as well as the necessary and sufficient condition for the possibility to extend a given k-form from such a surface to a harmonic k-form in the domain. A formula for the square of the singular Cauchy transform is given. The proofs of all these facts are based on a close relation between algebra-valued null-solutions of the Dirac operator in the Euclidean space and hyperholomorphic functions of Clifford analysis.
Idioma original | Inglés |
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Páginas (desde-hasta) | 1-20 |
Número de páginas | 20 |
Publicación | Georgian Mathematical Journal |
Volumen | 14 |
N.º | 1 |
DOI | |
Estado | Publicada - 2007 |
Publicado de forma externa | Sí |