Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates

• William Alexandre ^[1] ; Emmanuel Mazzilli ^[1]
  1. [1] Universit´e Lille 1, France
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 1, 2015, págs. 293-330
• Idioma: inglés
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• Resumen

  • 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.