Geodesic
Embeddings and widths of weighted Sobolev classes
Eurasian mathematical journal, Tome 6 (2015) no. 3, pp. 93-100.

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In this paper, embedding theorems for reduced weighted Sobolev classes $\hat{W}_{p,g}^r(\Omega)$ in Lebesgue spaces $L_{q,v}(\Omega)$ are obtained. Here weight functions have singularity at the origin and $v\notin L_q(\Omega)$. For some special weight functions order estimates for Kolmogorov, Gelfand and linear widths are obtained. 
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A. A. Vasil'eva. Embeddings and widths of weighted Sobolev classes. Eurasian mathematical journal, Tome 6 (2015) no. 3, pp. 93-100. http://geodesic.mathdoc.fr/item/EMJ_2015_6_3_a6/

[1] G. Bennett, “Some elementary inequalities, III”, Quart. J. Math. Oxford Ser., 42:166 (1991), 149–174 | DOI | MR | Zbl

[2] M. Sh. Birman, M. Z. Solomyak, “Piecewise polynomial approximations of functions of classes $W_p^\alpha$”, Math. USSR-Sb., 2:3 (1967), 295–317 | DOI | MR | Zbl

[3] R. A. DeVore, R. C. Sharpley, S. D. Riemenschneider, “$n$-widths for $C_p^\alpha$ spaces”, Anniversary volume on approximation theory and functional analysis (Oberwolfach, 1983), Internat. Schriftenreihe Numer. Math., 65, Birkhäuser, Basel, 1984, 213–222 | DOI | MR

[4] E. D. Gluskin, “Norms of random matrices and diameters of finite-dimensional sets”, Math. USSR-Sb., 48:1 (1984), 173–182 | DOI | MR | Zbl

[5] B. S. Kashin, “The widths of certain finite-dimensional sets and classes of smooth functions”, Math. USSR-Izv., 11:2 (1977), 317–333 | DOI | Zbl

[6] A. Kufner, H. P. Heinig, “The Hardy inequality for higher-order derivatives”, Trudy Mat. Inst. Steklov, 192, 1990, 105–113 (in Russian) | MR

[7] T. Mieth, “Entropy and approximation numbers of embeddings of weighted Sobolev spaces”, J. Appr. Theory, 192 (2015), 250–272 | DOI | MR | Zbl

[8] T. Mieth, Entropy and approximation numbers of weighted Sobolev spaces via bracketing, arXiv: 1509.00661v1

[9] Yu. G. Reshetnyak, “Integral representations of differentiable functions in domains with a nonsmooth boundary”, Sibirsk. Mat. Zh., 21:6 (1980), 108–116 (in Russian) | MR | Zbl

[10] Yu. G. Reshetnyak, “A remark on integral representations of differentiable functions of several variables”, Sibirsk. Mat. Zh., 25:5 (1984), 198–200 (in Russian) | MR | Zbl

[11] V. D. Stepanov, “Weighted norm inequalities of Hardy type for a class of integral operators”, J. London Math. Soc., 50:1 (1994), 105–120 | DOI | MR | Zbl

[12] V. M. Tikhomirov, “Diameters of sets in functional spaces and the theory of best approximations”, Russian Math. Surveys, 15:3 (1960), 75–111 | DOI | MR | Zbl

[13] V. M. Tikhomirov, “Theory of approximations”, Contemporary problems in mathematics. Fundamental directions. Itogi Nauki i Tekhniki, 14, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., M., 1987, 103–260 | MR

[14] H. Triebel, Interpolation theory. Function spaces. Differential operators, Dtsch. Verl. Wiss., Berlin, 1978 ; Mir, M., 1980 | MR | Zbl

[15] H. Triebel, “Entropy and approximation numbers of limiting embeddings, an approach via Hardy inequalities and quadratic forms”, J. Approx. Theory, 164:1 (2012), 31–46 | DOI | MR | Zbl

[16] A. A. Vasil'eva, “Kolmogorov widths and approximation numbers of Sobolev classes with singular weights”, Algebra i Analiz, 24:1 (2012), 3–39 (in Russian) | MR

[17] A. A. Vasil'eva, “Widths of weighted Sobolev classes on a John domain: strong singularity at a point”, Rev. Mat. Compl., 27:1 (2014), 167–212 | DOI | MR | Zbl