Geodesic
On Cesàro and Abel Summability Factors for Integrals
Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 453-477

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

Many results have been obtained about factors transforming integrals summable by ordinary and absolute Cesàro methods of non-negative orders into integrals summable by such methods (see [4], [2], [6], [3]) and also into integrals summable by the ordinary and absolute Abel methods (see [7]). Since the Cesàro summability methods (C, α) and |C, α| for integrals are defined for α ≦ –1, it is natural to try to extend the above mentioned results for α ≦ 0 to the case –1 ≧ α < 0. In this paper we restrict attention to the simplest case α = –1, and classify the summability factors from (C, –1) and |C, –1| to (C, –1) , |C, –1|, (C, λ), |C, λ|, A and |A|, where λ ≦ 0 and A denotes Abel summability. 
Borwein, David; Thorpe, Brian. On Cesàro and Abel Summability Factors for Integrals. Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 453-477. doi: 10.4153/CJM-1986-023-1
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