Singular Sums of Squares of Degenerate Vector Fields

Abstract

We simplify and give an alternative proof of hypoellipticity for generalizations of the singular sum of squares of complex vector fields studied by Kohn, with an appendix by Derridj and Tartakoff, in the Annals of Mathematics, vol. 162 no. 2, 2005, pp. 943-986. The main generalization is that the complex vector fields now come from domains of finite type. We also prove real analytic hypoellipticity and the optimality of our estimates.