Regularity of the Bergman Projection on Forms and Plurisubharmonicity Conditions

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Regularity of the Bergman Projection on Forms and Plurisubharmonicity Conditions

A function f ∈ C(Ω) is holomorphic on Ω, if it satisfies the CauchyRiemann equations: ∂̄f = ∑n k=1 ∂f ∂z̄k dz̄k = 0 in Ω. Denote the set of holomorphic functions on Ω by H(Ω). The Bergman projection, B0, is the orthogonal projection of square-integrable functions onto H(Ω)∩L2(Ω). Since the Cauchy-Riemann operator, ∂̄ above, extends naturally to act on higher order forms, we can as well define Bergm...

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ژورنال

عنوان ژورنال: Mathematische Annalen

سال: 2006

ISSN: 0025-5831,1432-1807

DOI: 10.1007/s00208-006-0005-y