Hi! I want to show the following: Let $\displaystyle u \in \, C^2(\mathbb{R}^3 \times (0,\infty))$ solve:
$\displaystyle u_{tt}-\triangle u=0$ on $\displaystyle \mathbb{R}^3 \times (0,\infty)$
$\displaystyle u=g, \, u_t=h$ on $\displaystyle \mathbb{R}^3 \times \{t=0\}$ with $\displaystyle g, h $ having compact support. Then there exists $\displaystyle C>0$, so that $\displaystyle |u(x,t)|\leq \frac{C}{t}$.

I know that a solution is given by $\displaystyle u(x,t)=\frac{1}{4 \pi t^2} \int_{\partial B(x,t)}^{} th(y)+g(y)+Dg(y) \cdot (y-x) dS(y)$, with $\displaystyle \partial B(x,t)$ meaning the boundary of the ball around $\displaystyle x$ with radius $\displaystyle t$.

Does anybody see this estimate?