Minkowski dimension and cauchy transform in Clifford analysis

Abstract:

In the present paper we provide some conditions of a geometrical character for continuous extendibility of the Clifford-Cauchy transform to the boundary of a domain in the Euclidean space of higher dimensions if its density satisfies a Hölder condition. The criterion obtained in this work is an extension to a very general class of domains of a result, which has already become classical, obtained by Viorel Iftimie, who proved in 1965, for the case of a domain with compact Liapunov boundary, that the Clifford-Cauchy transform has Hölder-continuous limit values for any Hölder-continuous density. © 2007 Birkhäuser Verlag Basel/Switzerland.

Año de publicación:

2007

Keywords:

• Geometric measure theory
• Cauchy transform
• Clifford analysis

Fuente:

scopus