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

Abstract

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 H"ormander 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 H"ormander type, thus providing a microlocal version, in the analytic category, of a result due to M. Derridj.

Keywords

• sums of squares of vector fields
• global analytic hypoellipticity
• treves conjecture
• local gevrey hypoellipticity
• microlocal regularity
• analytic vectors