About upper bound of the distribution function

Abstract

It is necessary to study Sobolev’s weighting space embedding into the Lebesgue space in the research of the elliptic operators. There exist a number of numerical characteristics for such embeddings. Approximate numbers are one of them. An upper bound of the distribution function of the approximate numbers of Sobolev’s weighting space into the Lebesgue space is proved in this paper. Basic definitions related to notion of the distribution function of the approximate numbers are considered by us. Estimates of the appropriate embedding operator are obtained for this function. The result obtained can be employed in the study of the spectral properties of self - adjoint differential operators