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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- Vasil’eva, A.A. Russ. J. Math. Phys. (2009) 16: 543. doi:10.1134/S1061920809040098
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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.