Advertisement

An integral representation and embedding theorems in the plane for multianisotropic spaces

  • G. A. Karapetyan
Functional Analysis

Abstract

The present paper is a continuation of the author’s paper [1], where by means of a special integral representation of functions we prove embedding theorems for multianisotropic functional spaces. In contrast to [1], here we consider the case where the corresponding completely regular polyhedron has many anisotropy vertices.

Keywords

Embedding theorem multianisotropic space completely regular polyhedron integral representation 

MSC2010 numbers

32Q40 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. A. Karapetyan, “Integral representations of functions and embedding theorems for multianisotropic spaces on the plane with one anisotropy vertex”, Journ. Contemp. Math. Analysis, 51 (6), 23–42, 2016.CrossRefzbMATHGoogle Scholar
  2. 2.
    S. L. Sobolev, “Sur un theoreme d’analyse fonctionnelle”, Mat. sb., 4(36) (3), 471–497, 1938.zbMATHGoogle Scholar
  3. 3.
    S. M. Nikol’skii, “On a problem of S. L. Sobolev”, Sib. Mat. J., 3 (6), 845–857, 1962.Google Scholar
  4. 4.
    K. T. Smith, “Inequalities for formally positive integro-differential forms”, Bull. Amer. Math., 368–370, 1961.Google Scholar
  5. 5.
    V. P. Il’in, “Integral representations of differentiable functions and their applications to the questions of extension of functions of the classes W p l(G)”, Sib. Mat. J., 8(3), 573–586, 1967.MathSciNetGoogle Scholar
  6. 6.
    O. V. Besov, “On coercivity in nonisotropic Sobolev spaces”, Mat. sb., 73(115) (4), 585–599, 1967.Google Scholar
  7. 7.
    O. V. Besov, V. P. Il’in, S. M. Nikol’skii, Integral representations of functions and embedding theorems (Moscow, Nauka, 1975).zbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Russian-Armenian UniversityYerevanArmenia

Personalised recommendations