  A space of entire functions of several complex variables rapidly decreasing
on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is
majorized with the help of a family of weight functions is considered in this
paper. For such space an equivalent description in terms of estimates on all of
its partial derivatives as functions on ${\mathbb R}^n$ and a Paley-Wiener type
theorem are obtained.
