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Geometric properties of infinite graphs and the Hardy-Littlewood maximal operator

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.

preprint2016arXivOpen access
Javier SoriaPedro Tradacete
math.COmath.CA
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Javier SoriaPedro Tradacete

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