English

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

Analysis of PDEs 2023-11-27 v1

Abstract

We prove a smooth and Gevrey-ss 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-ss wave front set in terms of the decay of this partial F.B.I. transform.

Keywords

Cite

@article{arxiv.2311.14547,
  title  = {Smooth and Gevrey Microlocal Hypoellipticity for a Class of Hypocomplex Tube Structures},
  author = {Nicholas Braun Rodrigues},
  journal= {arXiv preprint arXiv:2311.14547},
  year   = {2023}
}