Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 393-401
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Yu. A. Dubinskii. Nontriviality of Sobolev spaces of infinite order for a full Euclidean space and a torus. Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 393-401. http://geodesic.mathdoc.fr/item/SM_1976_29_3_a6/
@article{SM_1976_29_3_a6,
author = {Yu. A. Dubinskii},
title = {Nontriviality of {Sobolev} spaces of infinite order for a~full {Euclidean} space and a~torus},
journal = {Sbornik. Mathematics},
pages = {393--401},
year = {1976},
volume = {29},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1976_29_3_a6/}
}
TY - JOUR
AU - Yu. A. Dubinskii
TI - Nontriviality of Sobolev spaces of infinite order for a full Euclidean space and a torus
JO - Sbornik. Mathematics
PY - 1976
SP - 393
EP - 401
VL - 29
IS - 3
UR - http://geodesic.mathdoc.fr/item/SM_1976_29_3_a6/
LA - en
ID - SM_1976_29_3_a6
ER -
%0 Journal Article
%A Yu. A. Dubinskii
%T Nontriviality of Sobolev spaces of infinite order for a full Euclidean space and a torus
%J Sbornik. Mathematics
%D 1976
%P 393-401
%V 29
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1976_29_3_a6/
%G en
%F SM_1976_29_3_a6
In this paper we obtain necessary and sufficient conditions for nontriviality of the spaces $$ W^\infty\{a_\alpha,p_\alpha\}\equiv\biggl\{u(x):\rho(u)\equiv\sum_{|\alpha|=0}^\infty a_\alpha\|D^\alpha u\|^{p_\alpha}_{L_{r_\alpha}}<\infty\biggr\} $$ in the cases where the functions $u(x)$ are defined on $\mathbf R^n$ or are periodic with period $2\pi$ with respect to $n$ variables. Bibliography: 5 titles.
