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 $W^r_p$.
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