If $f\in L^p(T)$, then there exists $g\in L^p(T)$ such that $\hat{f}(n)=\hat{g}(n)$ for every $n\geq 0$

Question

If p>1, $f\in L^p(T)$, then there exists $g\in L^p(T)$ such that $\hat{f}(n)=\hat{g}(n)$ for every $n\geq 0$ and $\hat{g}(n)=0$ otherwise. I have not been able to come up with any ideas for this. Any help is appreciated. Thanks