2 problems

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The sharp variation bound for the discrete centered Hardy–Littlewood maximal function
Sharp variation conjecture. The constant in the inequality
Conjectureopenbounded-variation discrete-analysis hardy-littlewood-maximal-functionarXiv posted 2 days ago
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The p-ball formula conjecture for the modulus of continuity of the maximal function
Let $p\in(1,2)$ and $d\geq 2$ , and let $\omega$ be a modulus of continuity. Write $M$ for the uncentered Hardy–Littlewood maximal function and $\|M\|_{\operatorname{Op}(\omega)}$ f…
Conjectureopenhardy-littlewood-maximal-function lp-balls modulus-of-continuityarXiv posted 2 days ago

The sharp variation bound for the discrete centered Hardy–Littlewood maximal function