Fourier Coefficients of Functions with a Given Modulus of Continuity

In his letter to the Editor of "Mathematical Notes," the referee pointed out the incompleteness of the proof of Lemma 3. Indeed, the proof should have been provided with some reservations, which was not done.First, it should be noted the functions f taking negative values on [0, π/2] can be excluded.For functions f ∈ H[ω] that are nonnegative on [0, π/2], we denote