AlphaEvolve problems·alphaevolve:18
Hardy-Littlewood Maximal Inequality
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Let $C$ denote the best constant for which $$ \\left| \\{ x: \\sup_{h>0} \\frac{1}{2h} \\int_{x-h}^{x+h} f(y) dy \\geq \\lambda \\} \\right| \\leq \\frac{C}{\\lambda} \\int_\\mathbb{R} f(x) dx$$ for absolutely integrable non-negative $f \\colon \\mathbb{R} \\to \\mathbb{R}$. What is $C$?
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qed.bot, “Hardy-Littlewood Maximal Inequality”, https://qed.bot/t/alphaevolve-18, as of 30 Sep 2026.