A quantified Tauberian theorem for Laplace-Stieltjes transform

Abstract

We prove a quantified Tauberian theorem involving Laplace-Stieltjes transform which is motivated by the work of Ingham and Karamata. For this, we consider functions which are locally of bounded variation and, therefore, get a generalisation of some results of Batty and Duyckaerts. We show that our theorem can be applied to special Dirichlet series.