Bellman function sitting on a tree

TL;DR

This paper presents a Bellman function approach to prove key embedding inequalities on dyadic trees and extends the method to bi-trees, offering a new perspective on these mathematical structures.

Contribution

It introduces a formula-based proof method using Bellman functions for embedding inequalities on dyadic and bi-trees, expanding existing techniques.

Findings

Successful proof of embedding inequalities on dyadic trees

Extension of Bellman function method to bi-trees

Provides a new approach for analyzing tree-based structures

Abstract

In this note we give a proof-by-formula of certain important embedding inequalities on dyadic tree. This is done with the help of Bellman function. We also consider the case of a bi-tree, where a different approach is explained.