AlphaEvolve problems·alphaevolve:14
Hausdorff-Young Inequality
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For $1 \\leq p \\leq 2$, let $C(p)$ be the best constant such that $$ \\| \\hat f \\|_{L^{p'}(\\mathbb{R})} \\leq C(p) \\| f \\|_{L^p(\\mathbb{R})} $$ holds for all test functions $f \\colon \\mathbb{R} \\to \\mathbb{R}$. Here $p' \\coloneqq \\frac{p}{p-1}$ is the dual exponent of $p$. What is $C(p)$?
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qed.bot, “Hausdorff-Young Inequality”, https://qed.bot/t/alphaevolve-14, as of 30 Sep 2026.