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

authors

  • SORIA, JAVIER
  • TRADACETE PEREZ, PEDRO

publication date

  • March 2019

start page

  • 913

end page

  • 937

issue

  • 2

volume

  • 135

International Standard Serial Number (ISSN)

  • 0021-7670

Electronic International Standard Serial Number (EISSN)

  • 1565-8538

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.

subjects

  • Mathematics