Geodesic
The Simplest Tauberian Theorem
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 221-229.

Voir la notice de l'article provenant de la source Math-Net.Ru

The following problem is considered: obtain the asymptotic properties of a function $u$ from the asymptotic properties of the integral $\int_0^r{u(t)}dt$. As is well known, this can be done under additional constraints on the function $u(t)$. In this paper, we obtain a theorem in which these constraints are weaker than in other well-known versions of such theorems. 
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A. F. Grishin. The Simplest Tauberian Theorem. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 221-229. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a3/

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