Geometry of pseudo-convex domains of finite type with locally diagonalizable Levi form and Bergman kernel
In this paper, we give a precise description of the complex geometry of a pseudo-convex domain in C n near a boundary point of finite type where the Levi form is locally diagonalizable, and we use it to obtain sharp size estimates for the Bergman kernel and its derivatives. When all points of the bo...
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| Vydané v: | Journal de mathématiques pures et appliquées Ročník 85; číslo 1; s. 71 - 118 |
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| Jazyk: | English |
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| ISSN: | 0021-7824 |
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| Abstract | In this paper, we give a precise description of the complex geometry of a pseudo-convex domain in
C
n
near a boundary point of finite type where the Levi form is locally diagonalizable, and we use it to obtain sharp size estimates for the Bergman kernel and its derivatives. When all points of the boundary are of that type, we deduce from those estimates the
L
p
regularity of the Bergman projection.
On donne une description précise de la géométrie complexe d'un domaine pseudo-convexe de
C
n
au voisinage d'un point du bord de type fini où la forme de Levi est localement diagonalisable. On utilise cette description pour établir des estimations fines du noyau de Bergman ainsi que de ses dérivées. De ces estimations on déduit la régularité
L
p
du projecteur de Bergman lorsque tous les points du bord ont la propriété considérée. |
|---|---|
| AbstractList | In this paper, we give a precise description of the complex geometry of a pseudo-convex domain in
C
n
near a boundary point of finite type where the Levi form is locally diagonalizable, and we use it to obtain sharp size estimates for the Bergman kernel and its derivatives. When all points of the boundary are of that type, we deduce from those estimates the
L
p
regularity of the Bergman projection.
On donne une description précise de la géométrie complexe d'un domaine pseudo-convexe de
C
n
au voisinage d'un point du bord de type fini où la forme de Levi est localement diagonalisable. On utilise cette description pour établir des estimations fines du noyau de Bergman ainsi que de ses dérivées. De ces estimations on déduit la régularité
L
p
du projecteur de Bergman lorsque tous les points du bord ont la propriété considérée. |
| Author | Charpentier, Philippe Dupain, Yves |
| Author_xml | – sequence: 1 givenname: Philippe surname: Charpentier fullname: Charpentier, Philippe email: Philippe.Charpentier@math.u-bordeaux1.fr – sequence: 2 givenname: Yves surname: Dupain fullname: Dupain, Yves email: Yves.Dupain@math.u-bordeaux1.fr |
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| Cites_doi | 10.1007/BF01215657 10.2977/prims/1195180870 10.1007/BF02388789 10.2307/2007015 10.1016/0001-8708(90)90036-M 10.1353/ajm.2002.0003 10.2307/1971347 10.1007/BF02391775 10.1006/jmaa.1994.1379 10.1007/BF02621869 10.1007/BF01419622 10.1016/S0022-247X(03)00160-4 10.1002/cpa.3160180305 10.2140/pjm.2001.199.79 10.1215/S0012-7094-89-05822-5 10.1007/BF01450734 10.1007/PL00004593 10.1215/S0012-7094-78-04533-7 10.4134/JKMS.2002.39.3.425 10.1515/9781400883882 10.1007/BF02921594 10.1090/pspum/041/740872 10.2307/121013 10.1007/BF02395058 10.2307/1971487 10.1007/BF01168581 10.1017/S0027763000004992 10.4171/RMI/17 10.1007/BF02392539 10.1007/BF02921392 10.1017/S0027763000004414 10.1006/aima.1994.1082 10.1215/S0012-7094-94-07307-9 10.2307/1971240 10.2307/1971438 |
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| Keywords | Bergman kernel Finite type Plurisubharmonic functions Complex geometry Complex domain Convex geometry Kernel estimation Plurisubharmonic function Regularity Bergman kemel |
| Language | English |
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| SubjectTerms | Bergman kernel Complex Variables Convex and discrete geometry Exact sciences and technology Finite type Functions of a complex variable Geometry Mathematical analysis Mathematics Plurisubharmonic functions Sciences and techniques of general use Several complex variables and analytic spaces |
| Title | Geometry of pseudo-convex domains of finite type with locally diagonalizable Levi form and Bergman kernel |
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