Fourier multipliers and pseudo-differential operators on Fock-Sobolev spaces

Abstract

Any bounded linear operator $T$ on $L^2({\mathbb{R}}^n)$ gives rise to the operator $S=B\circ T\circ B^{\ast }$ on the Fock space $ \mathcal{F}(\C^n) $ where $B$ is the Bargmann transform. In this article we identify those $S$ which correspond to Fourier multipliers and pseudo-differential operators on $L^2({\mathbb{R}}^n)$ and study their boundedness on the Fock-Sobolev spaces $ \mathcal{F}^{s,2}(\C^n).$

arXiv comment18 pages