Three-dimensional analog of the Cauchy type integral

On a smooth closed surface, we consider integrals of the Cauchy type with kernel depending on the difference of arguments. They cover both double-layer potentials for second-order elliptic equations and generalized integrals of the Cauchy type for first-order elliptic systems. For the functions described by such integrals, we find sufficient conditions providing their continuity up to the boundary surface. We obtain the corresponding formulas for their limit values.