Sharp variational inequalities for the Hardy-Littlewood maximal operator on finite undirected graphs
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| Format: | Preprint |
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2026
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| _version_ | 1866917337717800960 |
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| author | González-Riquelme, Cristian Kovač, Vjekoslav Madrid, José |
| author_facet | González-Riquelme, Cristian Kovač, Vjekoslav Madrid, José |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp variational inequalities for the Hardy-Littlewood maximal operator on finite undirected graphs González-Riquelme, Cristian Kovač, Vjekoslav Madrid, José Classical Analysis and ODEs Combinatorics 26A45, 42B25, 39A12, 05C12 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. |
| title | Sharp variational inequalities for the Hardy-Littlewood maximal operator on finite undirected graphs |
| topic | Classical Analysis and ODEs Combinatorics 26A45, 42B25, 39A12, 05C12 |
| url | https://arxiv.org/abs/2603.12462 |