Carlson inequality

Let be non-negative numbers, not all zero. Then

(1)

Proved by F. Carlson [1]. The analogue of the Carlson inequality for integrals is: If , , then

(2)

The constant is best possible in the sense that there exists a sequence such that right-hand side of (1) is arbitrarily close to the left-hand side, and there exists a function for which (2) holds with equality.

References

[1]	F. Carlson, "Une inegalité" Ark. Math. Astron. Fys. , 25B : 1 (1934) pp. 1–5
[2]	G.H. Hardy, J.E. Littlewood, G. Pólya, "Inequalities" , Cambridge Univ. Press (1934)