C∞-hypoellipticity and extension of CR functions

• Mauro Nacinovich ^[2] ; Egmont Porten ^[1]
  1. [1] Mid Sweden University

     Mid Sweden University

     Suecia

     
  2. [2] Università di Roma “Tor Vergata”, Italy
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 3, 2015, págs. 677-703
• Idioma: inglés
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• Resumen

  • Let M be a CR submanifold of a complex manifold X. The main result of this article is to show that CR-hypoellipticity at p0 ϵ M is necessary and sufficient for holomorphic extension of all germs at p0 of CR functions on M to an ambient neighborhood of p0 in X. As an application, we obtain that CR-hypoellipticity implies the existence of global generic embeddings and prove holomorphic extension for a large class of CR manifolds satisfying a higher order Levi pseudoconcavity condition. We also obtain results on the relationship of holomorphic wedge-extension and the C∞-wave front set for CR distributions.