  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 a help of a family of weight functions (not radial in general)
is considered in the paper. For this space an equivalent description in terms
of estimates on all partial derivatives of functions on ${\mathbb R}^n$ and
Paley-Wiener type theorem are given.
