Summability of trigonometric Fourier series at -points and a generalization of the Abel-Poisson method

We study the convergence of linear means of the Fourier series of a function to as at all points at which the derivative exists (i. e. at the -points). Sufficient conditions for the convergence are stated in terms of the factors and, in the case of , in terms of the condition that the functions and belong to the Wiener algebra . We also study a new problem concerning the convergence of means of the Abel- Poisson type, , as depending on the growth of the function on the semi-axis. It turns out that cannot differ substantially from a power-law function.