The Clifford-Cauchy transform with a continuous density: N. Davydov's theorem

N. A. Davydov was among the first mathematicians who investigated the question of the continuity of the complex Cauchy transform along a non-smooth curve. In particular he proved that the Cauchy transform over an arbitrary closed, rectifiable Jordan curve can be continuously extended up to this curve from both sides if its density belongs to the Lipschitz class. In this paper we deal with higher dimensional analogue of Davydov's theorem within the framework of Clifford analysis.