Geodesic
Spaces of functions of positive smoothness on irregular domains
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 62-72

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The paper is devoted to constructing and studying spaces of functions of positive smoothness on irregular domains of the $n$-dimensional Euclidean space. We prove embedding theorems that connect the spaces introduced with the Sobolev and Lebesgue spaces. The formulations of the theorems depend on geometric parameters of the domain of definition of functions. 
@article{TM_2016_293_a3,
     author = {O. V. Besov},
     title = {Spaces of functions of positive smoothness on irregular domains},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {62--72},
     publisher = {mathdoc},
     volume = {293},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_293_a3/}
}
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%T Spaces of functions of positive smoothness on irregular domains
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2016
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%F TM_2016_293_a3
O. V. Besov. Spaces of functions of positive smoothness on irregular domains. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 62-72. http://geodesic.mathdoc.fr/item/TM_2016_293_a3/