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A note on an inequality with non-conjugate parameters

Published online by Cambridge University Press:  20 January 2009

P. L. Walker
P. L. Walker
Affiliation:
University of Lancaster
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The inequality

which is valid for positive, non-null f, g in the spaces Lp(0, ∞), Lq(0, ∞), where p > 1, (1/p)+(1/q) = 1, is a well-known generalisation of the classical inequality of Hilbert (see for instance Chapter 9 of Hardy, Littlewood, and Polya (1)).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 4 , December 1973 , pp. 293 - 294
Copyright
Copyright © Edinburgh Mathematical Society 1973

References

REFERENCES

(1) Hardy, Littlewood, and Polya, , Inequalities (Cambridge, 1934).Google Scholar
(2) Levin, V., On the two-parameter extension and analogue of Hilbert's inequality, J. London Math. Soc. 11 (1936), 119–124.CrossRefGoogle Scholar
(3) Bonsall, F. F., Inequalities with non-conjugate parameters, Quart. J. Math. Oxford Ser. (2) 2 (1951), 135–150.CrossRefGoogle Scholar