Spaces of Smooth Functions Generated by Nonhomogeneous Differential Expressions

A Sobolev-type embedding theorem is established, which differs from classical statements in that the assumptions are imposed on linear combinations of the form $\sum a_j D^{\alpha_j}f_j$ with different functions $f_j$ and different multi-indices $\alpha_j$. It is applied to a classification problem for spaces of smooth functions generated by finite collections of differential expressions.