When is $F(p)$ the Laplace transform of a bounded $f(t)$?

Abstract

Sufficient conditions are given for a function $F(p)$, analytic in Re$p>0$, to be a Laplace transform of a function $f(t)$, such that $ma{x}_{t\ge 0}|f(t)|<\infty$, $f(0)=0$.