Geodesic
On Absolute Summability by Riesz and Generalized Cesàro Means. II
Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 209-218

Voir la notice de l'article provenant de la source Cambridge University Press

1. We will use the terminology of part I [9], including the general assumptions of [9, § 1]. In that paper we had proved that |R, λ, κ| = |C, λ, κ| in case that κ is an integer. Now, we turn to non-integral orders κ.As to ordinary summation, the following inclusion relations (in the customary sense; see [9, end of § 1]) for non-integral κ have been established so far. (Since we are comparing Riesz methods of the same type λ and order κ only, (R, λ, κ) is written (R), etc., for the moment.) (R) ⊆ (C) is a result by Borwein and Russell [2]. (C) ⊆ (R) was proved by Jurkat [3] in the case 0 < κ < 1, and, after Borwein [1], it holds in the case 1 < κ < 2 if (1) (2) (i.e. decreases in the wide sense). 
Körle, H.-H. On Absolute Summability by Riesz and Generalized Cesàro Means. II. Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 209-218. doi: 10.4153/CJM-1970-027-3
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