On a One-Sided Tauberian Theorem: A Further Note

Abstract

My earlier note with the same title [3] was mainly about an extension of a theorem of Karamata on the Laplace- Abel transform to certain regular integral transforms Φ of a real function a(u) satisfying the classical one-sided condition,

a(u) u > - W, W > 0, for u > 1, and a(u) = 0 for u < 1. (1)