Schneider B.2023-06-162023-06-1620060041-59951573-9376https://doi.org/10.1007/s11253-006-0054-0https://hdl.handle.net/20.500.14365/3424Our main interest is an analog of a Cauchy-type integral for the theory of the Moisil-Theodoresco system of differential equations in the case of a piecewise-Lyapunov surface of integration. The topics of the paper concern theorems that cover basic properties of this Cauchy-type integral: the Sokhotskii-Plemelj theorem for it as well as a necessary and sufficient condition for the possibility of extending a given Hölder function from such a surface up to a solution of the Moisil-Theodoresco system of partial differential equations in a domain. A formula for the square of a singular Cauchy-type integral is given. The proofs of all these facts are based on intimate relations between the theory of the Moisil-Theodoresco system of partial differential equations and some versions of quaternionic analysis. © 2006 Springer Science+Business Media, Inc.eninfo:eu-repo/semantics/openAccessArticle10.1007/s11253-006-0054-02-s2.0-33744809259