When the Fourier transform is in $L^1(\mathbb{R}^n)$?

Question

When is the Fourier transform of a function in $L^1(\mathbb{R}^n)$? I only know that if $f$ is a Schwartz function, then $\widehat{f}$ It is also a function of Schwartz and therefore, it is in $L^1(\mathbb{R}^n)$ function, but asking that a function be Schwartz is a very strong assumption