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- 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- 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}
}