Bergman–Szegő kernel asymptotics in weakly pseudoconvex finite type cases

Chin-Yu Hsiao, Nikhil Savale

Type: Article

Publication Date: 2022-08-26

Citations: 9

DOI: https://doi.org/10.1515/crelle-2022-0044

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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>ℂ</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> {\mathbb{C}^{2}} , in agreement with D’Angelo’s example. Finally, our results generalize a three-dimensional CR embedding theorem of Lempert.

Locations

Journal für die reine und angewandte Mathematik (Crelles Journal) - View
arXiv (Cornell University) - View - PDF
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+	Spectral Asymptotics in the Semi-Classical Limit	1999	Mouez Dimassi Johannes Sjöstrand
+	Regularity properties of the \overline∂_{𝑏} equation on weakly pseudoconvex CR manifolds of dimension 3	1988	Michael Christ
+ PDF Chat	Boundary behavior of $\delta $ on weakly pseudo-convex manifolds of dimension two	1972	J. J. Kohn
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+	Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande. I.	1933	Stefan Bergmann
+ PDF Chat	Hypoelliptic differential operators and nilpotent groups	1976	Linda Preiss Rothschild E. M. Stein
+ PDF Chat	L2 estimates and existence theorems for the $\bar \partial $ operator	1965	Lars Hörmander
+	The range of the tangential Cauchy-Riemann operator	1986	J. J. Kohn
+	CR structures with group action and extendability of CR functions	1985	M. S. Baouendi Linda Preiss Rothschild E. Treves
+ PDF Chat	Boundary problems for pseudo-differential operators	1971	L. Boutet de Monvel