Regularity of the Bergman Projection on Forms and Plurisubharmonicity Conditions
نویسندگان
چکیده
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 Bergman projections on higher order forms: let Bj be the orthogonal projection of square-integrable (0, j)-forms onto its subspace of ∂̄-closed, square-integrable (0, j)-forms. In this paper we give a condition on Ω which implies that Bjf is smooth on Ω whenever f is. Our result is the following:
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