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

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 ∩ 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.