The aim of this paper is to prove a theorem of C. Miranda for the single and double layer potential corresponding to the fundamental solution of a second order differential operator with constant coefficients in Schauder spaces in the limiting case in which the open set is of class \(C^{m,1}\) and the densities are of class \(C^{m-1,1}\) for the single layer potential and \(C^{m,1}\) for the double layer potential for some nonzero natural number m. The treatment of the limiting case requires generalized Schauder spaces.