  An integral representation of the intertwining operator for the Dunkl
operators associated with symmetric groups is derived for the class of
functions of a single component. The expression provides a closed form formula
for the reproducing kernels of $h$-harmonics associated with symmetric groups
when one of the components is a coordinate vector. The latter allows us to
establish a sharp result for the Ces\`aro summability of $h$-harmonic series on
the unit sphere.
