Is Convolution's theorem on $L^2(\mathbb{R})$ valid?

Question

I know that, if $f,g \in L^1(\mathbb{R})$, then, $\widehat{f*g}=\widehat{f}\widehat{g}$ (Classical Convolution's theorem) . If $f,g\in L^2(\mathbb{R})$. Is this still valid?