Geodesic
Imbedding theorems and compactness for spaces of Sobolev type with weights. II
Sbornik. Mathematics, Tome 40 (1981) no. 1, pp. 51-77 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article theorems are established on imbedding and compactness for spaces of functions which are $p$th power summable with weight $\nu$ over the region $\Omega\subset\mathbf R^n$ and whose $m$th derivatives are $p$-summable with weight $\mu$ over $\Omega$. Moreover, necessary and sufficient conditions for the boundedness and compactness of the imbedding operator are obtained in terms of properties of the weight functions. The case of functions vanishing on the boundary is also considered. This article represents a continuation of previous research of the authors. Bibliography: 2 titles. 
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     author = {P. I. Lizorkin and M. Otelbaev},
     title = {Imbedding theorems and compactness for spaces of {Sobolev} type with {weights.~II}},
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P. I. Lizorkin; M. Otelbaev. Imbedding theorems and compactness for spaces of Sobolev type with weights. II. Sbornik. Mathematics, Tome 40 (1981) no. 1, pp. 51-77. http://geodesic.mathdoc.fr/item/SM_1981_40_1_a2/

[1] P. I. Lizorkin, M. Otelbaev, “Teoremy vlozheniya i kompaktnosti dlya prostranstv Sobolevskogo tipa s vesami”, Matem. sb., 108(150) (1979), 358–377 | MR | Zbl

[2] D. R. Adams, “A trace inequality for generalized potentials”, Studia Math., 48:1 (1973), 99–105 | MR | Zbl