On almost \((N,p,q)\) summability of conjugate Fourier series (Q5931266)

The authors claim to have proved a theorem on the almost generalized Nörlund summability of the conjugate series of a Fourier series. In their main theorem, they assume that \(\{p_n\}\) and \(\{q_n\}\) are monotonic nonincreasing sequences of real numbers such that \(R_n= \sum^n_{v=0} p_v q_{n-v}\to \infty\) as \(n\to\infty\), and \(\sum^n_{v=0} ({p_{n-v} q_v\over v+1})= O({R_n\over n})\). Choosing \(p_n= q_n=1\), \(R_n= n\to\infty\) but \(\sum^n_{v=0} {1\over v+1}\neq O(1)\).