ON (<i>p</i>,<i>l</i>)-CAPACITY, IMBEDDING 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 Lp. 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.

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