Published online by Cambridge University Press: 20 November 2018
Let f be an L integrable real valued function of period 2π and let
(1)
be its Fourier series. It is known that if f is of bounded variation then all nan and nbn(n=1,2,3,…) lie in the interval [-V(F)/π, V(F)/π;] where V(f) is the total variation of f. M. Izumi and S. Izumi [3] have recently asserted the following theorem A about the density of the positive and negative Fourier sine coefficients of a function of bounded variation.