Geodesic
On the Ranges of Certain Fractional Integrals
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1198-1216

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

Suppose 1 ≦ P < ∞, μ is real, and denote by L μ,p the collection of functions f, measurable on (0, ∞ ), and which satisfy 1.1 Also denote by [X] the collection of bounded operators from a Banach space X to itself. For v > 0, Re α > 0, Re β > 0, let 1.2 and 1.3 where ξ and η are complex numbers. Iv,α,ξ and Jv,β,η , are generalizations of the Riemann-Liouville and Weyl fractional integrals respectively, and consequently we shall refer to them as fractional integrals. 
Rooney, P. G. On the Ranges of Certain Fractional Integrals. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1198-1216. doi: 10.4153/CJM-1972-130-9
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