  Let ${T_1,...,T_l}$ be a collection of differential operators with constant
coefficients on the torus $\mathbb{T}^n$. Consider the Banach space $X$ of
functions $f$ on the torus for which all functions $T_j f$, $j=1,...,l$, are
continuous. Extending the previous work of the first two authors, we analyse
the embeddability of $X$ into some space $C(K)$ as a complemented subspace. We
prove the following. Fix some pattern of mixed homogeneity and extract the
senior homogeneous parts (relative to the pattern chosen) ${tau_1,...,tau_l}$
from the initial operators ${T_1,...,T_l}$. Let $N$ be the dimension of the
linear span of ${\tau_1,...,\tau_l}$. If $N\geqslant 2$, then $X$ is not
isomorphic to a complemented subspace of $C(K)$ for any compact space $K$.
  The main ingredient of the proof of this fact is a new Sobolev-type embedding
theorem.

Functional Analysis;Classical Analysis and ODEs