Carlson inequality

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


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


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.


[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)
How to Cite This Entry:
Carlson inequality. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098