A. S. Romanov, “Absolute continuity of functions in Sobolev spaces and modules of families of hypersurfaces elated to the Lorentz spaces”, Sib. J. Pure and Appl. Math., 2017, Volume 17, Issue 2,Pages <nobr>82

Absolute continuity of functions in Sobolev spaces and modules of families of hypersurfaces elated to the Lorentz spaces

A. S. Romanov^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: 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, Sobolev spaces, modulus of the family of hypersurfaces, absolute continuity.

UDC: 517.51

Received: 17.08.2016

DOI: 10.17377/PAM.2017.17.207