  We prove that a condition of boundedness of the maximal function of a
singular integral operator, that is known to be sufficient for the continuity
of the corresponding integral operator in H\"{o}lder spaces, is actually also
necessary in case the action of the integral operator does not decrease the
regularity of a function. We do so in the frame of metric measured spaces with
a measure satisfying certain growth conditions that include nondoubling
measures. Then we present an application to the case of an integral operator
defined on a compact differentiable manifold.
