About some method of extending of the function in spaces of Sobolev and Slobodetskii

The problem of extending of the function out the region considered in anisotropic spaces of Sobolev and Slobodetskii defined traces its derivatives on the boundary. Elements of the theory pseudodifferential operators, a special partition of unity of the dual variable are used in the proof of the theorem. The results can be applied in the study of a priory estimates in the boundary value problems for partial differential equations.