Young's Inequality

$ab\; \backslash le\; \backslash frac\{a^p\}\{p\}\; +\; \backslash frac\{b^q\}\{q\}.$

$\backslash log(ab)\; =\; \backslash log(a)+\backslash log(b)\; =\; \backslash log(a^\{p/p\})\; +\; \backslash log(b^\{q/q\})\; =\; \backslash frac\{\backslash log(a^p)\}\{p\}\; +\; \backslash frac\{\backslash log(b^q)\}\{q\}\; \backslash le\; \backslash log\backslash left(\backslash frac\{a^p\}\{p\}\; +\; \backslash frac\{b^q\}\{q\}\backslash right).$

p/p + b^q/q.

Usage

Young's inequality is used in the proof of the Hlder inequality.

 

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