Continuity of Gevrey\u2013H\xf6rmander pseudo-differential operators on modulation spaces

Abstract

Let sge 1, omega ,omega _0in {mathscr {P}}_{E,s}^0, ain Gamma _{s}^{(omega _0)}, and let {mathscr {B}} be a suitable invariant quasi-Banach function space. Then we prove that the pseudo-differential operator {text {Op}}(a) is continuous from M(omega _0omega ,{mathscr {B}}) to M(omega ,{mathscr {B}}).