On $(p,l)$-capacity, inbedding theorems, and the spectrum of a selfadjoint elliptic operator

Necessary and sufficient conditions are found for continuity, compactness, and closability of imbedding operators of some function spaces into the space $L_p$. These results (for $p=2$) give criteria for positive definiteness and discreteness of the spectrum of the Dirichlet problem for a selfadjoint elliptic operator of arbitrary order. Some integral inequalities are considered for differentiable functions on a cube.