Paper detail

On the microlocal regularity of the analytic vectors for "sums of squares" of vector fields

We prove via FBI-transform a result concerning the microlocal Gevrey regularity of analytic vectors for operators sums of squares of vector fields with real-valued real analytic coefficients of Hörmander type, thus providing a microlocal version, in the analytic category, of a result due to M. Derridj in "Local estimates for Hörmander's operators of first kind with analytic Gevrey coefficients and application to the regularity of their Gevrey vectors", concerning the problem of the local regularity for the Gevrey vectors for sums of squares of vector fields with real-valued real analytic/Gevrey coefficients. Nous démontrons , en utilisant la transformation de Fourier-Bros-Iagolnitzer, un résultat de régularité Gevrey microlocale , optimale, des vecteurs analytiques d'opérateurs de Hörmander de type "Sommes de carrés de champs de vecteurs" à coefficients analytiques sur un ouvert. Ce résultat est, dans le cadre analytique, la version microlocale du résultat de M.Derridj "Local estimates for Hörmander's operators of first kind with analytic Gevrey coefficients and application to the regularity of their Gevrey vectors", obtenu pour les vecteurs de Gevrey de tels opérateurs à coefficients Gevrey.