The Trace Theorem, the Luzin N- and Morse-Sard Properties for the Sharp Case of Sobolev-Lorentz Mappings

摘要

We prove Luzin N- and Morse-Sard properties for mappings of the Sobolev-Lorentz class , (this is the sharp case that guaranties the continuity of mappings). Our main tool is a new trace theorem for Riesz potentials of Lorentz functions for the limiting case . Using these results, we find also some very natural approximation and differentiability properties for functions in with exceptional set of small Hausdorff content.