We prove Luzin N- and Morse-Sard properties for mappings v : R n → R d of the Sobolev-Lorentz class W p , 1 k , p = n k (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 q = p . Using these results, we find also some very natural approximation and differentiability properties for functions in W p , 1 k with exceptional set of small Hausdorff content.
Keyphrases