On the Local Regularity of the Gevrey Vectors for Hörmander’s Operators

We study the local regularity of the analytic/Gevrey vectors for the general class of Hörmander’s operators, meaning those of degenerate elliptic type or of degenerate parabolic type \(P(x,D) = - \sum _{\ell =1}^{m} \left ( X_{\ell }(x,D)\right )^{2} + i X_{0}(x,D) + c(x)\) , thus improving the result obtained by M. Derridj in 2019 (Tunisian J Math 1(3):321–345, 2019). The optimal result in the degenerate elliptic case was obtained by the second author in 2019 (Pac J Math 302:511–543, 2019), and we obtain in this chapter optimal result in the degenerate parabolic case.