Anisotropic Gevrey-Hörmander pseudo-differential operators on modulation spaces

Abstract

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

15 pages. arXiv admin note: text overlap with arXiv:1805.03497, arXiv:1710.11366