Embedding theorems for multianisotropic spaces with two vertices of anisotropicity
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 29-37.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove embedding theorems for multianisotropic spaces in the case when the Newton polyhedron has two vertices of anisotropicity. The case of one anisotropicity vertex of the polyhedron was studied in previous papers of one of the authors. The present paper is the continuation of those.
Keywords: multianisotropic Sobolev spaces, integral representation, embedding theorems.
Mots-clés : multianisotropic polynomial
@article{UZERU_2017_51_1_a5,
     author = {G. A. Karapetyan and H. A. Petrosyan},
     title = {Embedding theorems for multianisotropic spaces with two vertices of anisotropicity},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {29--37},
     publisher = {mathdoc},
     volume = {51},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a5/}
}
TY  - JOUR
AU  - G. A. Karapetyan
AU  - H. A. Petrosyan
TI  - Embedding theorems for multianisotropic spaces with two vertices of anisotropicity
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2017
SP  - 29
EP  - 37
VL  - 51
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a5/
LA  - en
ID  - UZERU_2017_51_1_a5
ER  - 
%0 Journal Article
%A G. A. Karapetyan
%A H. A. Petrosyan
%T Embedding theorems for multianisotropic spaces with two vertices of anisotropicity
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2017
%P 29-37
%V 51
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a5/
%G en
%F UZERU_2017_51_1_a5
G. A. Karapetyan; H. A. Petrosyan. Embedding theorems for multianisotropic spaces with two vertices of anisotropicity. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 29-37. http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a5/

[1] Amer. Math. Soc. Transl., 1963, no. 2(34), 39—68 | Zbl | Zbl

[2] S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics, Novosibirsk, 1988 (in Russian)

[3] S. M. Nikolskii, “On a Problem of S.L. Sobolev.”, Sib. Math. Journal, 3:6 (1962), 845–857 (in Russian) | MR

[4] K. T. Smith, “Inequalities for Formally Positive Integro-Differential Forms”, Bull. Amer. Math. Soc., 67:4 (1961), 368–370 | DOI | MR | Zbl

[5] V. P. Il'in, “Integral Representations of Differentiable Functions and Their Application to Questions of Continuation of Functions of Classes $W^l_p(G)$”, Sib. Math. Journal, 8:3 (1967), 573–586 (in Russian) | MR | Zbl

[6] V. P. Il'in, “On inequalities between norms of partial derivatives of functions of several variables”, Proc. Numerical methods and inequalities in function spaces, Work collection, Trudy Mat. Inst. Steklov., 84, 1965, 144–173 (in Russian) | MR | Zbl

[7] Proc. Steklov Inst. Math., 117 (1972), 343–352 (in Russian) | MR | Zbl

[8] Math. USSR-Sb., 2:4 (1967), 521–534 | DOI | MR | Zbl

[9] O. V. Besov, V. P. Il’in, S. M. Nikolskii, Integral Representations of Functions and Embedding Theorems, Nauka, M., 1975, 480 pp. (in Russian) | MR | Zbl

[10] G. A. Karapetyan, “Integral Representation of Functions and Embedding Theorems for Multianisotropic Spaces on a Plane with One Vertex of Anisotropicity”, Journal of Contemporary Math. Analysis (Armenian Academy of Sciences), 51:6 (2016), 23–42 | MR

[11] G. A. Karapetyan, “Integral representation of functions and embedding theorems for multianisotropic spaces in the three-dimensional case”, Eurasian Math. J., 7:2 (2016), 19–37 | MR

[12] G.A. Karapetyan, “Integral Representation of Functions and Embedding Theorems for n-Dimensional Multianisotropic Spaces with One Vertex of Anisotropicity”, Sib. Math. Journal, 17 (2017) | MR