The Order of Fourier Coefficients of Function of Higher Variation
Rafat N. Siddiqi · Proceedings of the Japan Academy · 1972
This paper contains two theorems.First we estimate the order of Fourier coefficients of function of Wiener's class Vp which is strictly larger class than that of the class of functions of bounded variation.We have been able to find out the best constant which terms out to be V(f)12l/ in our case.The second theorem concerns about how many Fourier coefficients can have exactly the order n-lip.1. Let f be a real valued 27r-periodic function defined on [0, 27r] and let 0 = to < t1 < t2 <. .. < to = 2~r be a partition of [0, 2n].We write, for 1<p<oo,