Geodesic
Absolute continuity of functions in Sobolev spaces and modules of families of hypersurfaces elated to the Lorentz spaces
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 2, pp. 82-98 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study traces of functions In Sobolev–Lorentz spaces on Lipschitz hypersurfaces. We consider some aspects concerning the $(n-1)$-absolute continuity of functions.
Keywords: Lorentz spaces, modulus of the family of hypersurfaces, absolute continuity.
Mots-clés : Sobolev spaces 
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A. S. Romanov. Absolute continuity of functions in Sobolev spaces and modules of families of hypersurfaces elated to the Lorentz spaces. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 2, pp. 82-98. http://geodesic.mathdoc.fr/item/VNGU_2017_17_2_a6/

[1] E. M. Stein, G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, 1971 | MR | Zbl

[2] Kauhanen J., Koskela P., Maly J., “On Functions with Derivatives in a Lorentz Space”, Manuscripta Math., 100:1 (1999), 87–101 | DOI | MR | Zbl

[3] Stein E. M., “Editor's note: The differentiability of function in $R^n$”, Annals of Math., 113 (1981), 383–385 | MR | Zbl

[4] A. S. Romanov, “The continuity of Sobolev functions on the hyperplanes”, Sib. Elektron. Mat. Izv., 12 (2015), 832–841 (in Russian) | Zbl

[5] Fuglede B., “Extremal Lenght and Functional Completion”, Acta Math., 98:3–4 (1957), 171–219 | DOI | MR | Zbl

[6] A. S. Romanov, “The Holder continuity of Sobolev functions on the hypersurfaces”, Sib. Elektron. Mat. Izv., 13 (2016), 624–634 (in Russian) | Zbl

[7] A. S. Romanov, “Absolute continuity of the Sobolev type functions on metric spaces”, Sib. Math. J., 49:5 (2008), 913–918 | MR

[8] E. M. Stein, Singulr Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970 | MR

[9] Yu. G. Reshetnyak, “The concept of capacity in the theory of functions with generalized derivatives”, Sib. Math. J., 10:5 (1969), 818–842 | DOI | MR

[10] Federer H., Ziemer W. P., “The Lebesgue Set of a Function Whose Distributon Derivatives are $p$-th Summable”, Indiana Univ. Math. J., 22:2 (1972), 139–158 | DOI | MR | Zbl

[11] Hajlasz P., “Sobolev Spaces on an Arbitrary Metric Space”, Potential Anal., 1996, no. 5, 403–415 | MR | Zbl

[12] Stromberg J. O., Torchinsky A., Weighted Hardy Spaces, Lecture Notes in Math., 1381, Springer, Berlin etc., 1989, 193 pp. | DOI | MR | Zbl

[13] Hajlasz P., Kinnunen J., “Hölder Quasicontinuity of Sobolev Functions”, Rev. Math. Iberoamericana, 14:3 (1998), 601–622 | DOI | MR | Zbl