Nakhman A.D., Osilenker B.P.Regular Semi-Continuous Methods of Summation of Fourier Series // Scientific article. Journal "Transactions of the TSTU", vol. 23 , Tambov. TSTU publisher house , 2017. (pdf-file) Abstract: In this paper, using the semi-continuous summation methods, we build a class of means of Fourier series, that converge almost everywhere, as
well as in metrics of weighted spaces Lvp (v∈ Ap , p ≥ 1) and the space С of continuous periodic functions. It was found that a sufficient condition for such convergence, and the equity of weighting estimates of corresponding maximal operators, is the
generalized condition of B. Nagy. The results are applied to study of behavior of exponential means of Fourier series and include the cases of classical means of Cesaro, Riesz, and Abel-Poisson.