We shall determine non-isotropic Gevrey exponents for general Grushin operators based on the results given in the paper , where a method to determine isotropic (worst) Gevrey exponents was given. The ideas of the bracket calculus given in the paper  and FBI-transformation given in the paper  are also useful.
Cite this article
Yoshiaki Hashimoto, Takaaki Hoshino, Tadato Matsuzawa, Non-isotropic Gevrey Hypoellipticity for Grushin Operators. Publ. Res. Inst. Math. Sci. 38 (2002), no. 2, pp. 289–319DOI 10.2977/PRIMS/1145476339