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Communicated by W. Spr o ig SUMMARY N. A. Davydov was among the ÿrst 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, rectiÿable 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 Cli ord analysis.

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