Tohoku Mathematical Journal
2024
March
SECOND SERIES VOL. 76, NO. 1

Tohoku Math. J.
76 (2024), 1-85

Title ANALYTIC AND GEVREY REGULARITY FOR CERTAIN SUMS OF TWO SQUARES IN TWO VARIABLES

Author Antonio Bove

(Received March 11, 2022, revised June 9, 2022)
Abstract. We prove a Gevrey regularity theorem for the sum of squares of two vector fields in two variables with the assumption that the Hörmander bracket hypothesis is satisfied at length three. In Appendix A, a procedure is discussed for what attains to the possible optimality of the obtained Gevrey order.

Mathematics Subject Classification. Primary 35H10; Secondary 35H20, 35B65, 35A20, 35A27.
Key words and phrases. Sums of squares of vector fields, analytic and Gevrey hypoellipticity, Treves conjecture.

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