A Parametrix for Kohn’s Operator

Recently, Kohn constructed examples of sums of squares of complex vector fields satisfying Hörmander’s condition that lose derivatives, but are nevertheless hypoelliptic. He also demonstrated optimal L2 regularity. In this paper, we construct parametricies for Kohn’s operators, which lead to the corresponding Lp (1 < p < ∞) and Lipschitz regularity. In fact, our parametrix construction generalizes to a somewhat larger class of operators, yielding some new examples of operators which are hypoelliptic, but lose derivatives.