Geodesic
Embeddings of weighted Sobolev classes on a John domain
Eurasian mathematical journal, Tome 5 (2014) no. 3, pp. 129-134.

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In this paper, embedding theorems for weighted Sobolev classes are obtained. Here weights are functions of distance to some $h$-set. 
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A. A. Vasil'eva. Embeddings of weighted Sobolev classes on a John domain. Eurasian mathematical journal, Tome 5 (2014) no. 3, pp. 129-134. http://geodesic.mathdoc.fr/item/EMJ_2014_5_3_a9/

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[9] A. A. Vasil'eva, “Embedding theorem for weighted Sobolev classes on a John domain with weights that are functions of the distance to some $h$-set”, Russ. J. Math. Phys., 21:1 (2014), 112–122 | DOI

[10] A. A. Vasil'eva, Estimates for norms of two-weighted summation operators on a tree under some conditions on weights, arXiv: 1311.0375