Semielliptic Pseudodifferential Operators

This paper deals with boundary value problems for a class of semielliptic pseudodifferential operators. First we show how a factorization for the principal symbol of the pseudodifferential operator induces a factorization for the pseudodifferential operator itself. Such a factorization is used to set up a class of boundary value problems in a half space and to study regularity, up to the boundary, of the solutions. Our method relies on an explicit construction of parametrices for the boundary value problem.