Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 297-301
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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/
@article{MZM_1977_22_2_a13,
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},
year = {1977},
volume = {22},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a13/}
}
TY - JOUR
AU - S. Ya. Yakubov
AU - V. B. Shakhmurov
TI - Theorems on imbedding in anisotropic spaces of vector-valued functions
JO - Matematičeskie zametki
PY - 1977
SP - 297
EP - 301
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a13/
LA - ru
ID - MZM_1977_22_2_a13
ER -
%0 Journal Article
%A S. Ya. Yakubov
%A V. B. Shakhmurov
%T Theorems on imbedding in anisotropic spaces of vector-valued functions
%J Matematičeskie zametki
%D 1977
%P 297-301
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a13/
%G ru
%F MZM_1977_22_2_a13
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.
