AlphaEvolve problems·alphaevolve:16
Special Case of Gagliardo-Nirenberg Inequality
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Let $2 < p < \\infty$. Let $C(p)$ denote the supremum of the quantities $$ Q(f) \\coloneqq \\frac{\\|f\\|_{L^p(\\mathbb{R})}^{4p}}{\\|f\\|_{L^2(\\mathbb{R})}^{2(p+2)} \|f'\|_{L^2(\\mathbb{R})}^{2(p-2)}}$$ for all smooth rapidly decaying $f$, not identically zero. Establish upper and lower bounds for $C(p)$ that are as strong as possible.
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qed.bot, “Special Case of Gagliardo-Nirenberg Inequality”, https://qed.bot/t/alphaevolve-16, as of 30 Sep 2026.