Journal article

C8-hypoellipticity and extension of CR functions

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Publication Details

Author list: Porten, Egmont

Publication year: 2015

Start page: 677

End page: 703

Number of pages: 27

ISSN: 0391-173X

DOI: http://dx.doi.org/10.2422/2036-2145.201107_004

View additional information: View in Web of Science


Abstract

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.


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