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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:436

Article

Soria, Javier¹  Tradacete, Pedro² 

[1] Univ Barcelona, Dept Appl Math & Anal, Gran Via 585, E-08007 Barcelona, Spain

[2] Univ Carlos III Madrid, Dept Math, E-28911 Madrid, Spain

关键词: Finite graph;    Maximal operator;    l(p)-estimate;    Weak-type (1,1);   

DOI  :  10.1016/j.jmaa.2015.11.076

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free