Title: On the trace problem for Triebel--Lizorkin spaces with mixed norms,
Abstract: The subject is traces of Sobolev spaces with mixed Lebesgue norms on
Euclidean space. Specifically, restrictions to the hyperplanes given by the
first and last coordinates 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 except for the borderline cases; these are
also covered in case of the first variable. With respect to the first variable
the trace spaces are proved to be mixed-norm Lizorkin--Triebel spaces with a
specific sum exponent. For the last variable they are similarly defined Besov
spaces. The treatment includes continuous right-inverses and higher order
traces. The results rely on a sequence version of Nikolskij's inequality,
Marschall's inequality for pseudo-differential operators (and Fourier
multiplier assertions), as well as dyadic ball criteria.