Classification of simple bounded weight modules of the Lie algebra of vector fields on ${\text{C}}^n$

Let $W_n^{+}$ be the Lie algebra of the Lie algebra of vector fields on ${\text{C}}^n$. In this paper, we classify all simple bounded weight $W_n^{+}$ modules. Any such module is isomorphic to the simple quotient of a tensor module $F(P,M)=P\otimes M$forasimpleweightmodule$P$overtheWeylalgebra$K_n^+$ and a finite dimensional simple ${\text{gl}}_n$ module $M$.