On absolute Riesz and absolute Nörlund summability (Q1203461)

A study of the inclusion problem for \(| N,p|\subset| R,\lambda,k|\), \(k>0\), is taken up and a general theorem involving monotone functions \(p\) and \(\lambda\) is given. This theorem thus provides a counterpart of the theorem for the inclusion \(| R,\lambda,1|\subset| N,p|\) as given in [Indian J. Math. 7, 78-81 (1965; Zbl 0141.249); cf. also Rend. Circ. Mat. Palermo, II. Ser. 18, 49-61 (1969; Zbl 0232.40013)]. A corollary to the theorem shows that while some known classical results in the direction are obtainable from the theorem, some others stand generalized. A second theorem in the paper discusses the incomparability between certain Riesz and Nörlund methods.