If $f\in \mathbf{L}_{k}^{p}(\mathbf{R}^n) $ and $\varphi \in \mathscr{D}(\mathbf{R}^n)$, show that $\varphi\cdot f \in \mathbf{L}_{k}^{p}(\mathbf{R}^n)$.
How do you show this? I thought of using young's inequality or something along those lines but not sure on how to get started with it.