Bellman function for Hardy's inequality over dyadic trees
Abstract
In this article we use the Bellman function technique to characterize the measures for which the weighted Hardy's inequality holds on dyadic trees. We enunciate the (dual) Hardy's inequality over the dyadic tree and we use the associated "Burkholder-type" function to find the main inequality required in the proof of the result. We enunciate a "Bellman-type" function satisfying the required properties and we use the Bellman function technique to prove the main result of this article. We prove the optimality of the associated constant with an explicit example of an extremal family of maps. We also give an explicit interpretation of the corresponding Bellman function in terms of the theory of stochastic optimal control.
Fields of Study & Subjects
Advanced Banach Space Theory
Advanced Harmonic Analysis Research
Probability and Risk Models
Publication details
- Journal / source
- Journal of Functional Analysis
- Publisher
- Elsevier BV
- Volume
- 291
- Issue
- 5
- Pages
- 111557–111557
- Publication date
- 12 May 2026
- Language
- EN