proof of Young Inequality

By the concavity of the $\\log$ function we have

\\log ab=\\frac{1}{p}\\log a^{p}+\\frac{1}{q}\\log b^{q}\\leq\\log(\\frac{1}{p}a^{p}+%\\frac{1}{q}b^{q}).

By exponentiation we obtain the desired result.

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