Schneider, BShapiro, M2023-06-162023-06-1620040-7354-0209-40094-243Xhttps://hdl.handle.net/20.500.14365/3011International Workshop on Global Analysis -- APR 15-17, 2004 -- Cankaya Univ, Ankara, TURKEYWe study the analog of the Cauchy-type integral for the Laplace vector fields theory in case of a piece-wise Liapunov surface of integration and we prove the Sokhotski-Plemelj theorem for it as well as the necessary and sufficient condition for the possibility to extend a given Holder function from such a surface up to a Laplace vector field. Formula for the square of the singular Cauchy-type integral is given. The proofs of all these facts are based on intimate relations between Laplace vector field and some versions of quaternionic analysis.eninfo:eu-repo/semantics/closedAccessCauchy-type integralLaplace vector fields theoryquaternionic analysisConference Object