Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis

Abstract

A criterion for the existence of a continuous embedding of a weighted Sobolev class in a weighted Lp space is obtained, i.e., the existence of an index n for which the Kolmogorov n-diameter is finite. For the case in which a continuous embedding exists, the reduced Sobolev class is constructed together with a continuous operator of a natural embedding of the class in a weighted Lp-space.