Uniform bound for solutions of semilinear wave equations in $mathbb{R}^{1+3}$

We prove that solution of defocusing semilinear wave equation in $mathbb{R}^{1+3}$ with pure power nonlinearity is uniformly bounded for all $frac{3}{2}<pleq 2$ with sufficiently smooth and localized data. The result relies on the $r$-weighted energy estimate originally introduced by Dafermos and Rodnianski. This appears to be the first result regarding the global asymptotic property for the solution with small power $p$ under 2.