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Russian Mathematics

, Volume 62, Issue 11, pp 72–75 | Cite as

On Continuity of Functions With Generalized Derivatives

  • A. S. RomanovEmail author
Article
  • 14 Downloads

Abstract

We study the question of the continuity of functions for which the generalized gradient belongs to the Lorentz spaces.

Keywords

Sobolev space Lorentz space absolute continuity 

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References

  1. 1.
    Kauhanen, J., Koskela, P.,Maly, J. “On FunctionsWith Derivatives in a Lorentz Space”, ManuscriptaMath. 100, No. 1, 87–101 (1999).zbMATHGoogle Scholar
  2. 2.
    Stein, E., Weiss, G. Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, Princeton, 1971).zbMATHGoogle Scholar
  3. 3.
    Romanov, A. S. “The Hölder Continuity of Sobolev Functions on the Hypersurfaces”, Sib. Elektron.Mat. Izv. 13, 624–634 (2016).[in Russian].zbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Novosibirsk State University, Sobolev Institute of MathematicsSiberian Branch of the Russian Academy of SciencesNovosibirskRussia

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