SOBOLEV SPACES ASSOCIATED WITH A POLYHEDRON AND MULTI-QUASI-ELLIPTIC PSEUDODIFFERENTIAL-OPERATORS IN N-SPACE

In this note new classes of Sobolev spaces on R(n) are defined in connection with convex poliedrons in R2n. We establish a few properties of compact immersion and density. We turn then our consideration to pseudodifferential operators globally defined on R(n) and give sufficient conditions for these operators to be Fredholm operators acting on the Sobolev spaces previously defined. An explicit formula for the index, involving the logarithmic index of the symbol, is then given in the case of an ordinary differential operator.