  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.
