Poincaré inequalities on graphs

Abstract

We prove local $L^p$-Poincaré inequalities, $p\in [1,\infty ]$, on quasiconvex sets in infinite graphs endowed with a family of locally doubling measures, and global $L^p$-Poincaré inequalities on connected sets for flow measures on trees. We also discuss the optimality of our results.

13 pages, 1 figure

References in corpus (1)

• Analysis on trees with nondoubling flow measures