Conditions such that $f\leq g$ implies $FourierSeries(f)\leq FourierSeries(g)$

Question

Let $f$ and $g$ be continuous functions of period $2\pi$ and let $f\leq g$. I wonder the conditions on $f,g$ which guarantee the ineqality $FS(f)\leq FS(g)$, where $FS$ denote Fourier series of a function.