Integral representation and embedding theorems for n-dimensional multianisotropic spaces with one anisotropic vertex

Аннотация

We prove embedding theorems for the multianisotropic Sobolev spaces generated by the completely regular Newton polyhedron. Under study is the case of the polyhedron with one anisotropic vertex. We obtain a special integral representation of functions in terms of the tuple of multi-indices of the Newton polyhedron.