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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Vydáno v:	Journal de mathématiques pures et appliquées Ročník 85; číslo 1; s. 71 - 118
Hlavní autoři:	Charpentier, Philippe, Dupain, Yves
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Paris Elsevier SAS 2006 Elsevier
Témata:	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 Bergman kernel Finite type Plurisubharmonic functions Complex geometry Complex domain Convex geometry Kernel estimation Plurisubharmonic function Regularity Bergman kemel
ISSN:	0021-7824
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Popis
Shrnutí:	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.
ISSN:	0021-7824
DOI:	10.1016/j.matpur.2005.10.001