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arXiv · 1802.04033

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

William Alexandre·Emmanuel Mazzilli
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Abstract

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.

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William Alexandre, Emmanuel Mazzilli. 2018-02-12. Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates in strictly pseudoconvex domains of $C^n$. https://arxiv.org/abs/1802.04033

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