We consider complex-valued functions f∊L1(ℝ+), where ℝ+:=[0,∞), and prove sufficient conditions under which the sine Fourier transform and the cosine Fourier transform belong to one of the Lipschitz classes Lip (α) and lip (α) for some 0<α≦1, or to one of the Zygmund classes Zyg (α) and zyg (α) for some 0<α≦2. These sufficient conditions are best possible in the sense that they are also necessary if f(x)≧0 almost everywhere.
 Boas, R. P.Jr.1967Fourier series with positive coefficientsJ. Math. Anal. Appl.17463–483.