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Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates in strictly pseudoconvex domains of $\mathbb{C}^n$

Volume 124 / 2020

William Alexandre, Emmanuel Mazzilli Annales Polonici Mathematici 124 (2020), 209-245 MSC: 32A22, 32A26, 32A27, 32A37, 32A40, 32A55, 32C30, 32D15. DOI: 10.4064/ap181130-11-7 Published online: 27 March 2020

Abstract

Let $D$ be a strictly pseudoconvex domain and $X$ be a singular analytic set of pure dimension $n-1$ in $\mathbb{C} ^n$ 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 ${\rm BMO} (D)$. The extension is given by means of integral representation formulas and residue currents.

Authors

  • William AlexandreUniv. Lille
    CNRS
    UMR-8524 Laboratoire Paul Painlevé
    F-59000 Lille, France
    e-mail
  • Emmanuel MazzilliUniv. Lille
    CNRS
    UMR-8524 Laboratoire Paul Painlevé
    F-59000 Lille, France
    e-mail

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