AbstractThe subject is traces of Sobolev spaces with mixed Lebesgue norms on Euclidean space. Specifically, restrictions to the hyperplanes given by x1 = 0 and xn = 0 are applied to functions belonging to quasi‐homogeneous, mixed norm Lizorkin–Triebel spaces ; Sobolev spaces are obtained from these as special cases. Spaces admitting traces in the distribution sense are characterised up to the borderline cases; these are also covered in case x1 = 0. For x1 the trace spaces are proved to be mixed‐norm Lizorkin–Triebel spaces with a specific sum exponent; for xn they are similarly defined Besov spaces. The treatment includes continuous right‐inverses and higher order traces. The results rely on a sequence version of Nikol'skij's inequality, Marschall's inequality for pseudodifferential operators (and Fourier multiplier assertions), as well as dyadic ball criteria. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)