On a multi-weight inequality for the imbedding of anisotropic spaces

Abstract

In this paper we consider Sobolev spaces that are anisotropic in order of derivatives, in terms of summability and weight factors for these derivatives. The problems of embedding spaces of functions with various differential characteristics are relevant in connection with their important applications in the theory of differential operators, in numerical applied problems, in the study of approximate characteristics of integral operators acting in spaces of summable functions. The study was carried out by the localization method for estimating the norms of integral operators in weighted Lebesgue spaces. In this paper we obtain a multi - weight embedding theorem for anisotropic Sobolev spaces of general type.