Resumen de On the variation of the Hardy–Littlewood maximal functions on finite graphs

Feng Liu, Qingying Xue

• Let G be a connected and finite graph with the set of vertices V and the set of edges E. Let MG be the Hardy–Littlewood maximal function defined on graph G and Mα,G (0≤α<1) be its fractional version. In this paper, the regularity problems related to MG and Mα,G will be studied. We show that MG:BVp(G)→BVp(G) is bounded and Mα,G:ℓp(V)→BVq(G) is bounded and continuous for all 0