The authors study the (micro)hypoanalyticity and the Gevrey hypoellipticity of sums of squares of vector fields in terms of the Poisson-Treves stratification. The FBI transform is used. They prove hypoanalyticity for several classes of sums of squares and show that their method, though not general, includes almost every known hypoanalyticity result. Examples are discussed.

Table of Contents

• Introduction
• The Poisson-Treves stratification
• Standard forms for a system of vector fields
• Nested strata
• Bargman pseudodifferential operators
• The "a priori" estimate on the FBI side
• A single symplectic stratum
• A single nonsymplectic stratum
• Microlocal regularity in nested strata
• Known cases and examples
• Appendix A. A bracket lemma
• Appendix B. Nonsymplectic strata do not have the reproducing bracket property
• Bibliography
• Index