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This article is cited in 1 scientific paper (total in 1 paper)
On imbedding theorems for symmetric spaces
V. S. Klimov
Abstract:
In this report there are established embedding theorems for spaces of functions $u(x_1,\dots,x_n)$ whose generalized derivatives lie in a symmetric space $P(\Omega)$. There are found conditions for separability and reflexivity of the spaces $W^r_p(\Omega)$, and the question of the continuity and complete continuity of the embedding operator of $W^r_p(\Omega)$ into various spaces of functionals is studied. Under certain additional restrictions on the region $\Omega$ and the space $P$, there are proved embedding theorems for the spaces $W^r_p$.
Bibliography: 19 titles.
Received: 02.07.1969
Citation:
V. S. Klimov, “On imbedding theorems for symmetric spaces”, Mat. Sb. (N.S.), 82(124):3(7) (1970), 371–386; Math. USSR-Sb., 11:3 (1970), 339–353
Linking options:
https://www.mathnet.ru/eng/sm3456https://doi.org/10.1070/SM1970v011n03ABEH001297 https://www.mathnet.ru/eng/sm/v124/i3/p371
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Abstract page: | 383 | Russian version PDF: | 107 | English version PDF: | 23 | References: | 72 |
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