Best constants for the Hardy-Littlewood maximal operator on finite graphs Articles uri icon

authors

  • SORIA, JAVIER
  • TRADACETE PEREZ, PEDRO

publication date

  • April 2016

start page

  • 661

end page

  • 682

issue

  • 2

volume

  • 436

International Standard Serial Number (ISSN)

  • 0022-247X

Electronic International Standard Serial Number (EISSN)

  • 1096-0813

abstract

  • We study the behavior of averages for functions defined on finite graphs G, in terms of the Hardy-Littlewood maximal operator MG. We explore the relationship between the geometry of a graph and its maximal operator and prove that MG completely determines G (even though embedding properties for the graphs do not imply pointwise inequalities for the maximal operators). Optimal bounds for the p-(quasi)norm of a general graph G in the range 0 < p <= 1 are given, and it is shown that the complete graph K-n and the star graph S-n are the extremal graphs attaining, respectively, the lower and upper estimates. Finally, we study weak-type estimates and some connections with the dilation and overlapping indices of a graph. (C) 2015 Elsevier Inc. All rights reserved.

keywords

  • finite graph; maximal operator; l(p)-estimate; weak-type (1;1); metric spaces