#### 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, EDN: JWHHEK

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

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.

- 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). - 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). - 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 - 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 - 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). - 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 - Vladimirov V. S.
*Obobshchennye funktsii v matematicheskoy fizike*[Generalized Functions in Mathematical Physics]. Moscow, Nauka, 1976. 280 p. (in Russian). - 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.).

- 914 reads