Weighted estimates are obtained for the canonical solution to the equation in , where is a pseudoconvex domain, and is a strictly plurisubharmonic function. These estimates are then used to prove pointwise estimates for the Bergman projection kernel in . The weight is used to obtain a factor in the estimate of the kernel, where is the distance function in the Kähler metric given by the metric form .
Nous obtenons des estimations à poids pour la solution canonique de l’équation dans , où est un domaine pseudoconvexe et une fonction strictement plurisousharmonique. Ces estimations sont ensuite utilisées pour démontrer des estimations ponctuelles pour le noyau du projecteur de Bergman dans . Le poids est utilisé pour obtenir un facteur dans l’estimation du noyau, où est la distance associée à la métrique kählérienne définie par .
@article{AIF_1998__48_4_967_0, author = {Delin, Henrik}, 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}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {4}, year = {1998}, doi = {10.5802/aif.1645}, zbl = {0918.32007}, mrnumber = {99j:32027}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1645/} }
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 SP - 967 EP - 997 VL - 48 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1645/ DO - 10.5802/aif.1645 LA - en ID - AIF_1998__48_4_967_0 ER -
%0 Journal Article %A Delin, Henrik %T Pointwise estimates for the weighted Bergman projection kernel in ${\mathbb {C}}^n$, using a weighted $L^2$ estimate for the $\bar{\partial }$ equation %J Annales de l'Institut Fourier %D 1998 %P 967-997 %V 48 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1645/ %R 10.5802/aif.1645 %G en %F AIF_1998__48_4_967_0
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, Volume 48 (1998) no. 4, pp. 967-997. doi : 10.5802/aif.1645. https://aif.centre-mersenne.org/articles/10.5802/aif.1645/
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