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arXiv · 2009.07159

Bergman-Szeg\H{o} kernel asymptotics in weakly pseudoconvex finite type cases

Chin-Yu Hsiao·Nikhil Savale
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Abstract

We construct a pointwise Boutet de Monvel-Sj\"ostrand parametrix for the Szeg\H{o} 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.

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Chin-Yu Hsiao, Nikhil Savale. 2020-09-15. Bergman-Szeg\H{o} kernel asymptotics in weakly pseudoconvex finite type cases. https://doi.org/10.1515/crelle-2022-0044

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