  We provide a summary of the continuity 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 and Schauder
spaces on the boundary of a bounded open subset of ${\mathbb{R}}^n$.
  The purpose is two-fold. On one hand we try present in a single paper all the
known continuity results on the topic with the best known exponents in a
H\"{o}lder and Schauder space setting and on the other hand we show that many
of the properties we present can be deduced by applying results that hold in an
abstract setting of metric spaces with a measure that satisfies certain growth
conditions that include non-doubling measures as in a series of papers by
Garc\'{\i}a-Cuerva and Gatto in the frame of H\"{o}lder spaces and later by the
author.
