Essential differences of potential theories on a tree and on a bi-tree

In this note we give several counterexamples. One shows that small energy majorization on bi-tree fails. The second counterexample shows that energy estimate $\int _T {\mathbb{V}}^\nu _\varepsilon \, \mathrm{d}\nu \le C \varepsilon |\nu |$ always valid on a usual tree by a trivial reason (and with c...

Full description

Bibliographic Details
Main Authors: Mozolyako, Pavel, Volberg, Alexander
Format: Article
Language:English
Published: Académie des sciences 2022-09-01
Series:Comptes Rendus. Mathématique
Online Access:https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.362/