EXTENSION OF HOLOMORPHIC FUNCTIONS DEFINED ON SINGULAR COMPLEX HYPERSURFACES WITH GROWTH ESTIMATES IN STRICTLY PSEUDOCONVEX DOMAINS OF C n

Willliam Alexandre (1) , Emmanuel Mazzilli (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

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 ∩ D = ∅ and X ∩ bD is transverse. We give sufficient conditions for a function holomorphic on D ∩ X to admit a holomorphic extension which belongs to L q (D), q ∈ [1, +∞[, or to BM O(D). The extension is given by mean of integral representation formulas and residue currents.

Mots clés: Analytic spaces; Holomorphic extensions; Residue currents; Integral representations

Domaines: Variables complexes [math.CV]

Willliam Alexandre, Emmanuel Mazzilli. EXTENSION OF HOLOMORPHIC FUNCTIONS DEFINED ON SINGULAR COMPLEX HYPERSURFACES WITH GROWTH ESTIMATES IN STRICTLY PSEUDOCONVEX DOMAINS OF C n. Annales Polonici Mathematici, 2020, 124, pp.209-245. ⟨10.4064/ap181130-11-7⟩. ⟨hal-03256277v2⟩