Bergman–Szegő kernel asymptotics in weakly pseudoconvex finite type cases-Reference-Cited by-同舟云学术

Bergman–Szegő kernel asymptotics in weakly pseudoconvex finite type cases

Published:2022-08-27 Issue:791 Volume:2022 Page:173-223
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Hsiao Chin-Yu¹^ORCID,Savale Nikhil²^ORCID

Affiliation:

1. Institute of Mathematics , Academia Sinica , 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road , Taipei 10617 , Taiwan

2. Mathematisches Institut , Universität zu Köln , Weyertal 86–90, 50931 Köln , Germany

Abstract

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 ℂ 2

{\mathbb{C}^{2}}

, in agreement with D’Angelo’s example. Finally, our results generalize a three-dimensional CR embedding theorem of Lempert.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2022-0044/pdf

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