  Let $W_n^+$ be the Lie algebra of the Lie algebra of vector fields on $\C^n$.
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 $F(P,M)=P\otimes
M$ for a simple weight module $P$ over the Weyl algebra $K_n^+$ and a finite
dimensional simple $\gl_n$ module $M$.
