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

Abstract

Let $s\ge 1$, $\omega ,\omega_0\in \mathscr P_{E,s}^0$, $a\in \Gamma _{s}^{(\omega_0)}$, and let $\mathscr B$ be a suitable invariant quasi-Banach function space, Then we prove that the pseudo-differential operator $\operatorname{Op} (a)$ is continuous from $M(\omega_0\omega ,\mathscr B )$ to $M(\omega ,\mathscr B )$.