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Cāˆž-hypoellipticity and extension of CR functions
II Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
2015 (English)In: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. 14, no 3, 677-703 p.Article in journal (Refereed) Published
Abstract [en]

Let M be a CR submanifold of a complex manifold X. The main result of this article is to show that CR-hypoellipticity at p(0) is an element of M is necessary and sufficient for holomorphic extension of all germs at pc, of CR functions on M to an ambient neighborhood of p(0) 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-infinity-wave front set for CR distributions.

Place, publisher, year, edition, pages
2015. Vol. 14, no 3, 677-703 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-20583DOI: 10.2422/2036-2145.201107_004ISI: 000366338400001OAI: oai:DiVA.org:miun-20583DiVA: diva2:677469
Available from: 2013-12-09 Created: 2013-12-09 Last updated: 2016-01-07Bibliographically approved

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