Positive-Fourier-transform L1 bound
= Positive-Fourier-transform L1 bound
If $f\in L^1\cap L^\infty$ and $\widehat f\geq0$, testing against triangular frequency cutoffs and using monotone convergence gives $\lVert\widehat f\rVert_1\leq2\pi\lVert f\rVert_\infty$.