Anisotropic Gevrey-H\"ormander pseudo-differential operators on modulation spaces

We show continuity properties for the pseudo-differential operator $\mathrm{Op}(a)$ from $M({\omega }_0\omega ,\mathcal{B})$ to $M(\omega ,\mathscr B )$,forfixed$s,\sigma \ge 1$,$\omega ,\omega _0\in \mathscr P _{s,\sigma}^0$($\omega ,\omega _0\in \mathscr P {s,\sigma}$),$a\in \Gamma ^{\sigma,s}{(\omega 0)}$($a\in \Gamma ^{\sigma,s;0}{(\omega _0)}$),and$\mathscr B$ is an invariant Banach function space.