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Young's Inequality
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
(UMass Lowell)
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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.
PERMANENT CITATION
Ken Levasseur
"
Young's Inequality
"
http://demonstrations.wolfram.com/YoungsInequality/
Wolfram Demonstrations Project
Published: December 9, 2013
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