Sums of squares III: hypoellipticity in the infinitely degenerate regime

This is the third in a series of papers dealing with sums of squares and hypoellipticity in the infinitely degenerate regime. We establish a C^2,delta generalization of M. Christ's sum of squares theorem, and use a bootstrap argument with the sum of squares theorem for matrix functions in the second paper of this series, in order to prove a hypoellipticity theorem generalizing work in the infinitely degenerate regime to include nondiagonal operators and more general degeneracies.