On the Absolute Cesaro Summability of Negative Order of a Series Associated with the Conjugate Series of a Fourier Series

Abstract

1. Definition. Let λ ≡ λ(ω) be continuous, differentiable, and monotonie increasing in (0, ∞) and let it tend to infinity as ω → ∞. A series an is summable |R, λ, r|, where r > 0, ifwhere A is a fixed positive number (6, Definition B).Let f(t) be a periodic function with period 2π and Lebesgue integrable over (–π, π) and let1.1The series conjugate to (1.1), at t = x, is1.2