Weights of holomorphic extension and restriction

Let D ⊂⊂ C n 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 L 2-holomorphic function f on D to D′ is contained in L 2( D′, ϕ), and it is called a weight of extension, if any holomorphic function in...

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Bibliographic Details
Published in:Journal de mathématiques pures et appliquées Vol. 77; no. 7; pp. 697 - 719
Main Authors: Diederich, K., Herbort, G., Michel, V.
Format: Journal Article
Language:English
Published: Paris Elsevier SAS 01.09.1998
Elsevier
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Sciences and techniques of general use
Several complex variables and analytic spaces
Complex manifold
Manifold
Holomorphic function
Metric
Analytic space
Mathematical space
Analytical function
ISSN:0021-7824
Online Access:Get full text
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Summary:Let D ⊂⊂ C n 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 L 2-holomorphic function f on D to D′ is contained in L 2( D′, ϕ), and it is called a weight of extension, if any holomorphic function in L 2( D′, ϕ) can be extended to a L 2-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.
ISSN:0021-7824
DOI:10.1016/S0021-7824(98)80005-6