Comparison of the Bergman and Szegö kernels

Bo Yong Chen; Siqi Fu

doi:10.1016/j.aim.2011.07.013

Comparison of the Bergman and Szegö kernels

Bo Yong Chen
, Siqi Fu

The Rutgers Center for Computational and Integrative Biology (CCIB)

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

The quotient of the Szegö and Bergman kernels for a smooth bounded pseudoconvex domains in Cn is bounded from above by a constant multiple of δ|logδ|p for any p>n, where δ is the distance to the boundary. For a class of domains that includes those of D'Angelo finite type and those with plurisubharmonic defining functions, the quotient is also bounded from below by a constant multiple of δ|logδ|p for any p<-1. Moreover, for convex domains, the quotient is bounded from above and below by constant multiples of δ.

Original language	American English
Pages (from-to)	2366-2384
Number of pages	19
Journal	Advances in Mathematics
Volume	228
Issue number	4
DOIs	https://doi.org/10.1016/j.aim.2011.07.013
State	Published - Nov 10 2011

ASJC Scopus subject areas

General Mathematics

Keywords

32A25
32U35
32W05
Bergman kernel
Diederich-Fornæss exponent
L2-estimate
Pluricomplex Green function
Szegö kernel
∂-operator

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10.1016/j.aim.2011.07.013

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@article{f1a153d18b774f43a7198a7c63b8b68e,

title = "Comparison of the Bergman and Szeg{\"o} kernels",

abstract = "The quotient of the Szeg{\"o} and Bergman kernels for a smooth bounded pseudoconvex domains in Cn is bounded from above by a constant multiple of δ|logδ|p for any p>n, where δ is the distance to the boundary. For a class of domains that includes those of D'Angelo finite type and those with plurisubharmonic defining functions, the quotient is also bounded from below by a constant multiple of δ|logδ|p for any p<-1. Moreover, for convex domains, the quotient is bounded from above and below by constant multiples of δ.",

keywords = "32A25, 32U35, 32W05, Bergman kernel, Diederich-Forn{\ae}ss exponent, L2-estimate, Pluricomplex Green function, Szeg{\"o} kernel, ∂-operator",

author = "Chen, \{Bo Yong\} and Siqi Fu",

note = "Funding Information: ✩ Research supported in part by NSF grants DMS-0805852 and DMS-1101678, a U.S.–China Collaboration in Mathematical Research supplementary to NSF grant DMS-0500909, and by Fok Ying Tung Education Foundation grant No. 111004 and Chinese NSF grant No. 11031008. * Corresponding author at: Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA. E-mail addresses: [email protected] (B.-Y. Chen), [email protected] (S. Fu).",

year = "2011",

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doi = "10.1016/j.aim.2011.07.013",

language = "American English",

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T1 - Comparison of the Bergman and Szegö kernels

AU - Chen, Bo Yong

AU - Fu, Siqi

N1 - Funding Information: ✩ Research supported in part by NSF grants DMS-0805852 and DMS-1101678, a U.S.–China Collaboration in Mathematical Research supplementary to NSF grant DMS-0500909, and by Fok Ying Tung Education Foundation grant No. 111004 and Chinese NSF grant No. 11031008. * Corresponding author at: Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA. E-mail addresses: [email protected] (B.-Y. Chen), [email protected] (S. Fu).

PY - 2011/11/10

Y1 - 2011/11/10

N2 - The quotient of the Szegö and Bergman kernels for a smooth bounded pseudoconvex domains in Cn is bounded from above by a constant multiple of δ|logδ|p for any p>n, where δ is the distance to the boundary. For a class of domains that includes those of D'Angelo finite type and those with plurisubharmonic defining functions, the quotient is also bounded from below by a constant multiple of δ|logδ|p for any p<-1. Moreover, for convex domains, the quotient is bounded from above and below by constant multiples of δ.

AB - The quotient of the Szegö and Bergman kernels for a smooth bounded pseudoconvex domains in Cn is bounded from above by a constant multiple of δ|logδ|p for any p>n, where δ is the distance to the boundary. For a class of domains that includes those of D'Angelo finite type and those with plurisubharmonic defining functions, the quotient is also bounded from below by a constant multiple of δ|logδ|p for any p<-1. Moreover, for convex domains, the quotient is bounded from above and below by constant multiples of δ.

KW - 32A25

KW - 32U35

KW - 32W05

KW - Bergman kernel

KW - Diederich-Fornæss exponent

KW - L2-estimate

KW - Pluricomplex Green function

KW - Szegö kernel

KW - ∂-operator

UR - https://www.scopus.com/pages/publications/80052687356

UR - https://www.scopus.com/pages/publications/80052687356#tab=citedBy

U2 - 10.1016/j.aim.2011.07.013

DO - 10.1016/j.aim.2011.07.013

M3 - Article

SN - 0001-8708

VL - 228

SP - 2366

EP - 2384

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 4

ER -

Comparison of the Bergman and Szegö kernels

Abstract

ASJC Scopus subject areas

Keywords

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