 Convolution of L infinity and L1 functions

For $f\in L^{\infty }({\mathbb{R}}^n)$ and $g\in L^1({\mathbb{R}}^n)$,is bounded by $\Vert f{\Vert }_{\infty }\Vert g{\Vert }_1$. Continuity follows fromand continuity of translation in $L^1$.