Young's Inequality

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Given positive numbers and whose reciprocals add up to one, the product of two positive real numbers and is less than or equal to a weighted sum of and powers of and .

Contributed by: Ken Levasseur (December 2013)
(UMass Lowell)
Open content licensed under CC BY-NC-SA


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References

[1] R. B. Nelson, Proofs without Words II, More Exercises in Visual Thinking, Washington, DC: Mathematical Association of America, 2000.

[2] W. H. Young, "On Classes of Summable Functions and Their Fourier Series," Proceedings of the Royal Society A, 87, 1912 pp. 225–229.



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