  In this paper we consider a semi-linear, energy sub-critical, defocusing wave
equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensional
space with $p \in [3,5)$. We prove that if initial data $(u_0, u_1)$ are radial
so that $\|\nabla u_0\|_{L^2 ({\mathbb R}^3; d\mu)}, \|u_1\|_{L^2 ({\mathbb
R}^3; d\mu)} \leq \infty$, where $d \mu = (|x|+1)^{1+2\varepsilon}$ with
$\varepsilon > 0$, then the corresponding solution $u$ must exist for all time
$t \in {\mathbb R}$ and scatter. The key ingredients of the proof include a
transformation $\mathbf{T}$ so that $v = \mathbf{T} u$ solves the equation
$v_{\tau \tau} - \Delta_y v = - \left(\frac{|y|}{\sinh |y|}\right)^{p-1}
e^{-(p-3)\tau} |v|^{p-1}v$ with a finite energy, and a couple of global
space-time integral estimates regarding a solution $v$ as above.
