About the summation of Fourier series by Voronoi-Nerlund method
A measurable and Lebesgue integrable function f ( x ) belonging to the space Lp (1 ≤ p ≤ ∞) is considered. The question of the behavior of the Linear operator, or ( W,pn ) - Voronoi averages, which are formed using partial sums of order k of the Fourier series of the function f ( x ), is investigated. A statement is proved in which, for each n >1, an upper bound of the value p ( f ; x ; Wn ) is established through a sequence of the best approximations of the function in a uniform metric.