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

Abstract

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 Derridj (Pac J Math 302(2):511–543, 2019) 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.