  This paper brings results about the behavior of sequences of eigenvalues or
singular values of integral operators generated by square-integrable kernels on
the real m-dimensional unit sphere, $m\leq2$. Under smoothness assumptions on
the generating kernels, given via Laplace-Beltrami differentiability, we obtain
super-exponential decay rates for the eigenvalues of the generated positive
integral operators and for singular values of those integral operators which
are non-positive. We show an optimal-type result and provide a list of
parametric families of kernels which are of interest for numerical analysis and
geostatistical communities and satisfy the smoothness assumptions for the
positive case.
