POINCARE INEQUALITIES ON GRAPHS

被引：0

作者：

Levi, M. ^{[1
]}

Santagati, F. ^{[2
]}

Tabacco, A. ^{[2
]}

Vallarino, M. ^{[2
]}

机构：

[1] Univ Genoa, DIBRIS, MaLGa Ctr, Genoa, Italy

[2] Politecn Torino, Dipartimento Eccellenza 20182022, Dipartimento Sci Matemat Giuseppe Luigi Lagrange, Corso Duca Abruzzi 24, I-10129 Turin, Italy

来源：

ANALYSIS MATHEMATICA | 2023年 / 49卷 / 02期

关键词：

Poincare inequality; graph; tree; nondoubling measure; PARABOLIC HARNACK INEQUALITY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Every graph of bounded degree endowed with the counting measure satisfies a local version of L-p-Poincare inequality, p is an element of [1, infinity]. We show that on graphs which are trees the Poincare constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of L-p-Poincare inequality, despite the fact that they are nondoubling measures of exponential growth.

引用

页码：529 / 544

页数：16

共 16 条

[1] Local and non-local Poincare inequalities on Lie groups [J].