Geodesic
Theorems on imbedding in anisotropic spaces of vector-valued functions
Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 297-301.

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Imbedding theorems are proved for abstract anisotropic spaces of Sobolev type. In particular, it is proved that if $G$ is a bounded set satisfying the $l$ horn condition, then there holds the imbedding $$ D^\alpha W_2(G;H(A),H)\hookrightarrow L_2(G;H(A^1-|\alpha:l|)), $$ where $|\alpha:l|=\frac{\alpha_1}{l_2}+\dots+\frac{\alpha_n}{l_n}\le1$, $H$ is a Hilbert space, and $A$ is a self-adjoint positive operator. 
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     author = {S. Ya. Yakubov and V. B. Shakhmurov},
     title = {Theorems on imbedding in anisotropic spaces of vector-valued functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {297--301},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a13/}
}
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S. Ya. Yakubov; V. B. Shakhmurov. Theorems on imbedding in anisotropic spaces of vector-valued functions. Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 297-301. http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a13/