  In this note we give a proof of the Sobolev and Morrey embedding theorems
based on the representation of functions in terms of the fundamental solution
of suitable partial differential operators. We also prove the compactness of
the Sobolev embedding. We first describe this method in the classical setting,
where the fundamental solution of the Laplace equation is used, to recover the
classical Sobolev and Morrey theorems. We next consider degenerate Kolmogorov
equations. In this case, the fundamental solution is invariant with respect to
a non-Euclidean translation group and the usual convolution is replaced by an
operation that is defined in accordance with this geometry. We recover some
known embedding results and we prove the compactness of the Sobolev embedding.
We finally apply our regularity results to a kinetic equation.
