Abstract
In the present paper the sufficient conditions are obtained for the generalized r-absolute convergence (
{0<r<2}
) of the single Fourier trigonometric series in terms of the modulus of δ-variation of a function.
It is proved that these conditions are unimprovable in a certain sense.
The classical results of Berstein, Szasz, Zygmund and others, related to the absolute convergence of single trigonometric Fourier series, were previously generalized by [L. Gogoladze and R. Meskhia,
On the absolute convergence of trigonometric Fourier series,
Proc. A. Razmadze Math. Inst. 141 2006, 29–40].