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Soria de Diego, Francisco Javier Tradacete, Pedro 2024-01-17T17:15:26Z 2024-01-17T17:15:26Z 2019 Soria, J., Tradacete, P. Geometric properties of infinite graphs and the Hardy–Littlewood maximal operator. JAMA 137, 913–937 (2019). https://doi.org/10.1007/s11854-019-0019-5 2737-0690 10.1007/s11854-019-0019-5 https://hdl.handle.net/20.500.14352/93673 https://doi.org/10.1007/s11854-019-0019-5 https://link.springer.com/article/10.1007/s11854-019-0019-5 We study different geometric properties on infinite graphs, related to the weak-type boundedness of the Hardy–Littlewood maximal averaging operator. In particular, we analyze the connections between the doubling condition, having finite dilation and overlapping indices, uniformly bounded degree, the equidistant comparison property and the weak-type boundedness of the centered Hardy–Littlewood maximal operator. Several non-trivial examples of infinite graphs are given to illustrate the differences among these properties. eng open access Geometric properties of infinite graphs and the Hardy-Littlewood maximal operator journal article