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Journal d'Analyse Mathématique

, Volume 137, Issue 2, pp 913–937 | Cite as

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

  • Javier Soria
  • Pedro TradaceteEmail author
Article
  • 24 Downloads

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.

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© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of BarcelonaBarcelonaSpain
  2. 2.Instituto de Ciencias Matematicas (CSIC-UAM-UC3M-UCM)Consejo Superior de Investigaciones CientificasMadridSpain

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