On absolute weighted mean summability (Q1316332)

Using functional analytic techniques, the authors obtain the necessary and sufficient conditions in order that the series \(\sum a_ n\) should be summable \(| R, q_ n |_ k\), \(k \geq 1\), whenever it is summable \(| R, p_ n |\). The results contained in this paper extend the known results of \textit{L. S. Bosanquet} [published in the review in M. R. 11, 654 (1950) of the subsequently cited paper] and that of \textit{G. Sunouchi} [Tohoku Math. J., II. Ser. 1, 57-65 (1949; Zbl 0041.391)] to the case \(k>1\).