论文标题
Bergman-szegő弱假子有限型案例中的内核渐近学
Bergman-Szegő kernel asymptotics in weakly pseudoconvex finite type cases
论文作者
论文摘要
我们构造了一个弱假胞件的szegő内核的点孔de monvel-sjöstrand参数，假设有限类型的较弱的pseudoconvex三维Cr歧管，则假设其切向CR操作员要封闭；从而扩展了对基督的早期分析。这特别将伯格曼内核的Fefferman边界渐近学扩展到与D'Angelo的示例一致的$ \ Mathbb {C}^{2} $中弱的pseudoconvex域。最后，我们的结果概括了Lempert定理的三维CR嵌入。
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.
