Bergman Szego kernel asymptotics in weakly pseudoconvex finite type cases

We construct a pointwise Boutet de Monvel-Sjostrand parametrix for the Szego kernel of a weakly pseudoconvex three-dimensional CR manifold of finite type assuming the range of its tangential CR operator to be closed; thereby extending the earlier analysis of Christ. This particularly extends Fefferman's boundary asymptotics of the Bergman kernel to weakly pseudoconvex domains in C-2, in agreement with D'Angelo's example. Finally, our results generalize a three-dimensional CR embedding theorem of Lempert