On the summability |R, log ω, 1| of Fourier series and an associated series

Abstract

1. Definition. Let λ ≡ λ(ω) be continuous, differentiable and monotonic increasing in (0, ∞) and let it tend to infinity as ω → ∞. A series is summable |R, λ, r|, where r > 0, ifwhere A is a fixed positive number(3).