Bergman-Szegő kernel asymptotics in weakly pseudoconvex finite type cases

Abstract

We construct a pointwise Boutet de Monvel-Sjöstrand parametrix for the Szegő 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 ${\mathbb{C}}^2$, in agreement with D'Angelo's example. Finally our results generalize a three dimensional CR embedding theorem of Lempert.

References in corpus (1)

• On the asymptotic expansion of Bergman kernel

Cited by in corpus (1)

• Algebraic Bergman kernels and finite type domains in ${\mathbb{C}}^2$