Geometric properties of infinite graphs and the Hardy-Littlewood maximal operator
Classical Analysis and ODEs
2016-02-03 v1 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1602.01029,
title = {Geometric properties of infinite graphs and the Hardy-Littlewood maximal operator},
author = {Javier Soria and Pedro Tradacete},
journal= {arXiv preprint arXiv:1602.01029},
year = {2016}
}
Comments
18 pages, 5 figures