Pointwise estimates for the weighted Bergman projection kernel in ℂ n , using a weighted L 2 estimate for the ∂ ¯ equation

Henrik Delin

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 4, page 967-997
  • ISSN: 0373-0956

Abstract

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Weighted L 2  estimates are obtained for the canonical solution to the ∂ ‾ equation in L 2 ( ℂ n , e - φ d λ ) , where Ω is a pseudoconvex domain, and φ is a strictly plurisubharmonic function. These estimates are then used to prove pointwise estimates for the Bergman projection kernel in L 2 ( ℂ n , e - φ d λ ) . The weight is used to obtain a factor e - ϵ ρ ( z , ζ ) in the estimate of the kernel, where ρ is the distance function in the Kähler metric given by the metric form i ∂ ∂ ‾ φ .

How to cite

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Delin, Henrik. "Pointwise estimates for the weighted Bergman projection kernel in ${\mathbb {C}}^n$, using a weighted $L^2$ estimate for the $\bar{\partial }$ equation." Annales de l'institut Fourier 48.4 (1998): 967-997. <http://eudml.org/doc/75317>.

@article{Delin1998,
abstract = {Weighted $L^2$ estimates are obtained for the canonical solution to the $\bar\{\partial \}$ equation in $L^2(\{\Bbb C\}^n,e^\{-\varphi \}d\lambda )$, where $\Omega $ is a pseudoconvex domain, and $\varphi $ is a strictly plurisubharmonic function. These estimates are then used to prove pointwise estimates for the Bergman projection kernel in $L^2(\{\Bbb C\}^n,e^\{-\varphi \}d\lambda )$. The weight is used to obtain a factor $e^\{-\epsilon \rho (z,\zeta ) \}$ in the estimate of the kernel, where $\rho $ is the distance function in the Kähler metric given by the metric form $i\partial \bar\{\partial \}\varphi $.},
author = {Delin, Henrik},
journal = {Annales de l'institut Fourier},
keywords = {Bergman kernel; weighted Bergman spaces; Kähler metrics},
language = {eng},
number = {4},
pages = {967-997},
publisher = {Association des Annales de l'Institut Fourier},
title = {Pointwise estimates for the weighted Bergman projection kernel in $\{\mathbb \{C\}\}^n$, using a weighted $L^2$ estimate for the $\bar\{\partial \}$ equation},
url = {http://eudml.org/doc/75317},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Delin, Henrik
TI - Pointwise estimates for the weighted Bergman projection kernel in ${\mathbb {C}}^n$, using a weighted $L^2$ estimate for the $\bar{\partial }$ equation
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 4
SP - 967
EP - 997
AB - Weighted $L^2$ estimates are obtained for the canonical solution to the $\bar{\partial }$ equation in $L^2({\Bbb C}^n,e^{-\varphi }d\lambda )$, where $\Omega $ is a pseudoconvex domain, and $\varphi $ is a strictly plurisubharmonic function. These estimates are then used to prove pointwise estimates for the Bergman projection kernel in $L^2({\Bbb C}^n,e^{-\varphi }d\lambda )$. The weight is used to obtain a factor $e^{-\epsilon \rho (z,\zeta ) }$ in the estimate of the kernel, where $\rho $ is the distance function in the Kähler metric given by the metric form $i\partial \bar{\partial }\varphi $.
LA - eng
KW - Bergman kernel; weighted Bergman spaces; Kähler metrics
UR - http://eudml.org/doc/75317
ER -

References

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