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On Continuity of Functions With Generalized Derivatives

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Abstract

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

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References

  1. Kauhanen, J., Koskela, P.,Maly, J. “On FunctionsWith Derivatives in a Lorentz Space”, ManuscriptaMath. 100, No. 1, 87–101 (1999).

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  2. Stein, E., Weiss, G. Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, Princeton, 1971).

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  3. Romanov, A. S. “The Hölder Continuity of Sobolev Functions on the Hypersurfaces”, Sib. Elektron.Mat. Izv. 13, 624–634 (2016).[in Russian].

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Authors and Affiliations

  1. Novosibirsk State University, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Acad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. S. Romanov

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  1. A. S. Romanov
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Correspondence to A. S. Romanov.

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Original Russian Text © A.S. Romanov, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 11, pp. 82–85.

Submitted by S.K. Vodop’yanov

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Romanov, A.S. On Continuity of Functions With Generalized Derivatives. Russ Math. 62, 72–75 (2018). https://doi.org/10.3103/S1066369X18110087

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  • DOI: https://doi.org/10.3103/S1066369X18110087

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