Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Malyutina A. N. On the continuity of some classes and subclasses of maps with an s-averaged characteristic. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 3, pp. 287-292. DOI: 10.18500/1816-9791-2022-22-3-287-292

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2022
Full text:
(downloads: 346)
Language: 
Russian
Heading: 
Article type: 
Article
UDC: 
517.98
EDN: 
JWHHEK

On the continuity of some classes and subclasses of maps with an s-averaged characteristic

Autors: 
Malyutina Aleksandra Nikolaevna, Tomsk State University
Abstract: 

According to the well-known theorem of S. L. Sobolev, if $G$ is a bounded domain of Euclidean space and a function is a function having the first generalized derivatives summable with degree  $p$, then it is continuous in $G$. If $1<p\le n$  this property, generally speaking, may not be. In this paper, we find the necessary conditions under which some classes and subclasses of maps with an $s$-averaged characteristic will be continuous. Examples of subclasses of such mappings with the above properties are given in our papers.

References: 
  1. Sobolev S. L. Nekotorye primeneniya funktsional’nogo analiza v matematicheskoy fizike [Some Applications of Functional Analysis in Mathematical Physics]. Leningrad, LSU Publ., 1950. 255 p. (in Russian).
  2. Nikulina N. G. On the continuity of a class of functions. In: V. V. Chernikov (ed.) Extreme Problems of the Theory of Functions. Tomsk, Tomsk State University Publ., 1980, pp. 78–83 (in Russian).
  3. Asanbekov U. K., Malyutina A. N. Calculation of the module of a spherical ring. Complex Analysis and Its Applications: Proceedings of the VIII Petrozavodsk International Conference (Petrozavodsk, 2016, July 3–9). Petrozavodsk, PetrSU Publ., 2016, pp. 103–106 (in Russian). EDN: WLTYKX
  4. Alipova K., Elizarova M., Malyutina A. Examples of the mappings with s-averaged characteristic. Complex Analysis and Its Applications: Proceedings of the VII Petrozavodsk International Conference (Petrozavodsk, 2014, June 29 – July 5). Petrozavodsk, PetrSU Publ., 2014, pp. 12–17. EDN: SIDYGZ
  5. Nikolsky S. M. Priblizhenie funktsiy mnogikh peremennykh i teoremy vlozheniya [Approximation of Functions of Several Variables and Embedding Theorems]. Moscow, Nauka, 1969. 455 p. (in Russian).
  6. Malyutina A. N., Asanbekov U. K. On the module of continuity of mappings with an s-averaged characteristic. Tomsk State University Journal of Mathematics and Mechanics, 2019, no. 59, pp. 11–15 (in Russian). https://doi.org/10.17223/19988621/59/2, EDN: GLUSCA
  7. Vladimirov V. S. Obobshchennye funktsii v matematicheskoy fizike [Generalized Functions in Mathematical Physics]. Moscow, Nauka, 1976. 280 p. (in Russian).
  8. Stein E. M. Singular Integrals and Differentiability Properties of Functions. Princeton, NJ, Princeton University Press, 1970. 288 p. (Russ. ed.: Moscow, Mir, 1973. 342 p.).
Received: 
12.03.2022
Accepted: 
15.04.2022
Published: 
31.08.2022