Let $u \in C^{\infty}_c(\Bbb{R}^d)$, where $C^{\infty}_c(\Bbb{R}^d)$ is the family of infintly differentiable functions with a compact support.
Is $u$ in $L^2(\Bbb{R}^d)$?
I think that $u$ is in $L^2(\Bbb{R}^d)$ since $u$ has compact support.
Let $u \in C^{\infty}_c(\Bbb{R}^d)$, where $C^{\infty}_c(\Bbb{R}^d)$ is the family of infintly differentiable functions with a compact support.
Is $u$ in $L^2(\Bbb{R}^d)$?
I think that $u$ is in $L^2(\Bbb{R}^d)$ since $u$ has compact support.