no. 4
Pointwise estimates for the weighted Bergman projection kernel in ℂ n , using a weighted L 2 estimate for the ∂ ¯ equation
Annales de l'Institut Fourier, Tome 48 (1998) no. 4, pp. 967-997

Weighted L 2  estimates are obtained for the canonical solution to the ∂ ¯ equation in L 2 (ℂ n ,e -ϕ dλ), 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 dλ). The weight is used to obtain a factor e -ϵρ(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.

Nous obtenons des estimations L 2 à poids pour la solution canonique de l’équation ∂ ¯ dans L 2 (ℂ n ,e -ϕ dλ), où Ω est un domaine pseudoconvexe et ϕ une fonction strictement plurisousharmonique. Ces estimations sont ensuite utilisées pour démontrer des estimations ponctuelles pour le noyau du projecteur de Bergman dans L 2 (ℂ n ,e -ϕ dλ). Le poids est utilisé pour obtenir un facteur e -ϵρ(z,ζ) dans l’estimation du noyau, où ρ est la distance associée à la métrique kählérienne définie par i∂∂ ¯ϕ.

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     title = {Pointwise estimates for the weighted {Bergman} projection kernel in ${\mathbb {C}}^n$, using a weighted $L^2$ estimate for the $\bar{\partial }$ equation},
     journal = {Annales de l'Institut Fourier},
     pages = {967--997},
     year = {1998},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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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, Tome 48 (1998) no. 4, pp. 967-997. doi: 10.5802/aif.1645

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