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.