Theorems on imbedding in anisotropic spaces of vector-valued functions

Imbedding theorems are proved for abstract anisotropic spaces of Sobolev type. In particular, it is proved that if $G$ is a bounded set satisfying the $l$ horn condition, then there holds the imbedding
$$ D^\alpha W_2(G;H(A),H)\hookrightarrow L_2(G;H(A^1-|\alpha:l|)), $$
where $|\alpha:l|=\frac{\alpha_1}{l_2}+\dots+\frac{\alpha_n}{l_n}\le1$, $H$ is a Hilbert space, and $A$ is a self-adjoint positive operator.