We prove the validity of regularizing properties of the boundary integral
operator corresponding to the double layer potential associated to the
fundamental solution of a {\em nonhomogeneous} second order elliptic
differential operator with constant coefficients in H\"{o}lder spaces by
exploiting an estimate on the maximal function of the tangential gradient with
respect to the first variable of the kernel of the double layer potential and
by exploiting specific imbedding and multiplication properties in certain
classes of integral operators and a generalization of a result for integral
operators on differentiable manifolds.Comment: arXiv admin note: substantial text overlap with arXiv:2305.19672,
arXiv:2103.06971, arXiv:2307.0415