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arXiv · 2603.12462

Sharp variational inequalities for the Hardy-Littlewood maximal operator on finite undirected graphs

Cristian González-Riquelme·Vjekoslav Kovač·José Madrid
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Abstract

We study sharp $p$-variational inequalities for the Hardy-Littlewood maximal operator on complete graphs, answering in the affirmative a question by Feng Liu and Qingying Xue. We also use computational assistance to find sharp constants in $1$-variational inequalities for all connected graphs on at most five vertices and pose a conjecture on the corresponding sharp constants for path graphs. Finally, we construct finite graphs with arbitrarily large $p$-variational constants.

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Cristian González-Riquelme, Vjekoslav Kovač, José Madrid. 2026-03-12. Sharp variational inequalities for the Hardy-Littlewood maximal operator on finite undirected graphs. https://arxiv.org/abs/2603.12462

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