So how do you prove if $f, g\in L^2(\mathbb{T})$, then $f*g\in \mathbb{A}(\mathbb{T})$. $\mathbb{T}$ denote $[0,1)$ and $\mathbb{A}(\mathbb{T})$ denote the Wiener algebra such that if $f\in \mathbb{A}(\mathbb{T})$, then $$\sum_{n=-\infty}^\infty |\widehat{f}(n)|<\infty$$ We define $$||f||_{\mathbb{A}}=\sum_{n\in\mathbb{Z}}|\hat{f}(n)|$$
I know that $\widehat{f*g}=\widehat{f}\widehat{g}$, but how can this help