On the regularity of the solutions and of analytic vectors for “sums of squares”

We present a brief survey on some recent results concerning the local and global regularity of the solutions for some classes/models of sums of squares of vector fields with real-valued real analytic coefficients of Hormander type. Moreover we also illustrate 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 Hormander type, thus providing a microlocal version, in the analytic category, of a result due to M. Derridj.