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- W4287780692 abstract "Let $G=(V,E)$ be a finite graph and $M_G$ be the centered Hardy-Littlewood maximal operator defined there. We find the optimal value $bf{C}_{G,p}$ such that the inequality $$text{Var}_{p}(M_{G}f)leq {textbf{C}}_{G,p}text{Var}_{p}(f)$$ holds for every $f:Vto mathbb{R},$ where $text{Var}_p$ stands for the $p$-variation, when: (i) $G=K_n$ (complete graph) and $pin [frac{log(4)}{log(6)},infty)$ or $G=K_4$ and $pin (0,infty)$; (ii) $G=S_n$ (star graph) and $1ge pge frac{1}{2}$; $pin (0,frac{1}{2})$ and $nge C(p)$ or $G=S_3$ and $pin (1,infty).$ We also find the value of the norm $|M_{G}|_{2}$ when: (i) $G=K_n$ and $nge 3$; (ii) $G=S_n$ and $nge 3.$" @default.
- W4287780692 created "2022-07-26" @default.
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- W4287780692 date "2020-05-06" @default.
- W4287780692 modified "2023-10-16" @default.
- W4287780692 title "Sharp Inequalities for maximal operators on finite graphs" @default.
- W4287780692 doi "https://doi.org/10.48550/arxiv.2005.03146" @default.
- W4287780692 hasPublicationYear "2020" @default.
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