Abstract. We prove an inequality for sums, which generalizes both Landau's sharpening of Carlson's inequality and the corresponding complementary result by Levin and Stečkin. The inequality is optimal, in the sense that necessary and sufficient conditions on the parameters for which the inequality holds are given. In some cases, sharp constants are obtained, also in situations not covered by the classical results.

AMS Subject Classification (1991): 26D15

Keyword(s): Inequalities, Landau inequality, Levin--Stečkin inequality

Received June 26, 2003. (Registered under 5796/2009.)