, Volume 16, Issue 4, pp 543-562
Date: 13 Dec 2009

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

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Abstract

A criterion for the existence of a continuous embedding of a weighted Sobolev class in a weighted L p 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 L p -space.

This work was supported by the program “Leading Scientific Schools” (grant no. NSh-3233.2008.1).