Traces on surfaces for function classes with dominant mixed derivatives

Spaces of Sobolev type are considered in which the principal part of the norm is determined by mixed derivatives. Theorems on the imbedding of such spaces in the space $L_2(S)$ are established; $S$ is a surface of codimension 1. The imbedding conditions depend on the order of tangency of the surface $S$ with hyperplanes parallel to certain coordinate axes.