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arXiv · 2311.14547

Smooth and Gevrey Microlocal Hypoellipticity for a Class of Hypocomplex Tube Structures

Nicholas Braun Rodrigues
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Abstract

We prove a smooth and Gevrey-$s$ microlocal hypoellipticity result for a system of complex vector fields associated with a real-analytic locally integrable structure of tube type, that is also microlocal hypocomplex. In order to so, we employ the use of a certain partial F.B.I. transform adapted to the locally integrable structure, first introduced by M. S. Baouendi, C. H. Chang and F. Treves, and we prove a microlocal characterization of the smooth and Gevrey-$s$ wave front set in terms of the decay of this partial F.B.I. transform.

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Nicholas Braun Rodrigues. 2023-11-24. Smooth and Gevrey Microlocal Hypoellipticity for a Class of Hypocomplex Tube Structures. https://arxiv.org/abs/2311.14547

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