  In this paper, we study the Gevrey regularity of spatially homogeneous
Boltzmann equation without angular cutoff. We prove the propagation of Gevrey
regularity for $C^\infty$ solutions with the Maxwellian decay to the Cauchy
problem of spatially homogeneous Boltzmann equation. The idea we use here is
based on the framework of Morimoto's recent paper (See Morimoto: J.
Pseudo-Differ. Oper. Appl. (2010) 1: 139-159, DOI:10.1007/s11868-010-0008-z),
but we extend the range of the index $\gamma$ satisfying $\gamma + 2s \in
(-1,1)$, $s\in (0,1/2)$ and in this case we consider the kinetic factor in the
form of $\Phi(v)=|v|^\gamma$ instead of $\la v \ra ^\gamma$ as Morimoto did
before.
