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. ∂ |α|h ∂ǫ 1 α 1 ...∂ǫn αn = 0 on X ∩ D for all multi-index α with 0 < |α| ≤ k, then h has a holomorphic extension H in L q (D) when q < +∞ and in BM O(D) when q = +∞. Moreover, up to a uniform multiplicative constant depending only on k and N , the