On the sharpness of inequalities concerning Dirichlet series and integrals (Q1379845)

\textit{H. P. Mulholland} [Proc. Lond. Math. Soc., II. Ser. 29, 281-292 (1929; JFM 55.0202.02)] established some inequalities for the Dirichlet series \(\sum^\infty_{n= 2} a_n n^{-x-1}\) and related integrals \(\int^\infty_0 a(x)n^{-x}dx\). In previous papers, \textit{L. Leindler} [Acta Sci. Math. 57, No. 1-4, 401-418 (1993; Zbl 0797.40002); ibid. 58, No. 1-4, 281-297 (1993; Zbl 0793.40005)] generalized both the discrete and integral inequalities of Mulholland. In this paper, the author shows that his generalizations in the previous papers cannot be improved on.