Cauchy transform on nonrectifiable surfaces in Clifford analysis

The problem of reconstructing a monogenic Clifford algebra valued function on the boundary Γ of a general open set Ω   in Rn+1Rn+1 from a prescribed jump data u over the boundary is deeply connected with the study of the Clifford–Cauchy transform(CΓu)(x):=∫Γy−x¯σn|y−x|n+1n(y)u(y)dy,x∉Γ. Necessary and sufficient condition on non-rectifiable Γ is established guaranteeing the existence of continuous boundary values of this transform for all functions satisfying a Hölder type condition.