Weights of holomorphic extension and restriction

AbstractLet D ⊂⊂Cn be a domain and D′ ⊂ D a closed complex submanifold. A normalized weight function ϕ on D′ is called weight of restriction, if the restriction of any L2-holomorphic function f on D to D′ is contained in L2(D′, ϕ), and it is called a weight of extension, if any holomorphic function in L2(D′, ϕ) can be extended to a L2-holomorphic function on D. Properties of the families of weights of restriction and weights of extension and relations between them are studied in this article. An application to the boundary behavior of the Bergman metric is given