Universität zu Köln

Hsiao, Chin-Yu and Savale, Nikhil ORCID: 0000-0001-7331-4527 (2022). Bergman Szego kernel asymptotics in weakly pseudoconvex finite type cases. J. Reine Angew. Math., 2022 (791). S. 173 - 224. BERLIN: WALTER DE GRUYTER GMBH. ISSN 1435-5345

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Abstract

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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hsiao, Chin-Yu UNSPECIFIED UNSPECIFIED UNSPECIFIED Savale, Nikhil UNSPECIFIED orcid.org/0000-0001-7331-4527 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-664595
DOI:	10.1515/crelle-2022-0044
Journal or Publication Title:	J. Reine Angew. Math.
Volume:	2022
Number:	791
Page Range:	S. 173 - 224
Date:	2022
Publisher:	WALTER DE GRUYTER GMBH
Place of Publication:	BERLIN
ISSN:	1435-5345
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language BOUNDARY-BEHAVIOR; CR-STRUCTURES; MARGIN Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66459