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# CR Extension from Manifolds of Higher Type

Published:2008-12-01
Printed: Dec 2008
• Luca Baracco
• Giuseppe Zampieri
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## Abstract

This paper deals with the extension of CR functions from a manifold $M\subset \mathbb C^n$ into directions produced by higher order commutators of holomorphic and antiholomorphic vector fields. It uses the theory of complex sectors'' attached to real submanifolds introduced in recent joint work of the authors with D. Zaitsev. In addition, it develops a new technique of approximation of sectors by smooth discs.
 MSC Classifications: 32V25 - Extension of functions and other analytic objects from CR manifolds 32V35 - Finite type conditions on CR manifolds 32C16 - unknown classification 32C1632F18 - Finite-type conditions