Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates in strictly pseudoconvex domains of \(C^n\)

Let \(D\) be a strictly pseudoconvex domain and \(X\) be a singular analytic set of pure dimension \(n-1\) in \(C^n\) such that \(X\cap D\neq \emptyset\) and \(X\cap bD\) is transverse. We give sufficient conditions for a function holomorphic on \(D\cap X\) to admit a holomorphic extension which bel...

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Bibliographic Details
Published in:arXiv.org 2018-02
Main Authors: Alexandre, William, Mazzilli, Emmanuel
Format: Article
Language:English
Subjects:
Analytic functions
Domains
Hyperspaces
Mathematical analysis
Online Access:Get full text
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Summary:Let \(D\) be a strictly pseudoconvex domain and \(X\) be a singular analytic set of pure dimension \(n-1\) in \(C^n\) such that \(X\cap D\neq \emptyset\) and \(X\cap bD\) is transverse. We give sufficient conditions for a function holomorphic on \(D\cap X\) to admit a holomorphic extension which belongs to \(L^q(D),\) \(q\in [1,+\infty[\), or to \(BMO(D)\). The extension is given by mean of integral representation formulas and residue currents.
ISSN:2331-8422