Real analytic dependence of simple and double layer potentials uponperturbation of the support and of the density

We consider a hypersurface in Eucledian space ${\mathbf{R}}^{n}$ parametrized by a diffeomorphism of the unit sphere to ${\mathbf{R}}^{n}$, and a density function on the hypersurface, which we think as points in suitable Schauder spaces, and we consider the dependence of the corresponding simple and double layer potentials, which we also think as points in suitable Schauder spaces, upon variation of the diffeomorphism and of the density, and we show a real analyticity theorem for such dependence.