Resumen de Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates
William Alexandre, Emmanuel Mazzilli
Let D be a strictly convex domain and X be a singular complex hypersurface in Cn such that X \ D 6= ; and X \ bD is transverse. We first give necessary conditions for a function holomorphic on D\X to admit a holomorphic extension belonging to Lq (D), with q 2 [1,+1]. When n = 2 and q < +1, we then prove that this condition is also sufficient. When q = +1we prove that this condition implies the existence of a BMO-holomorphic extension. In both cases, the extensions are given by mean of integral representation formulas and new residue currents.
