Dimension‐Independent Functional Inequalities by Tensorization and Projection Arguments
Abstract
ABSTRACT We study stability under tensorization and projection‐type operations of gradient estimates and other functional inequalities for Markov semigroups on metric spaces. Using transportation inequalities obtained by Baudoin and Eldredge in 2021, we prove that constants in the gradient estimates can be chosen to be dimension‐independent. Our results are applicable to hypoelliptic diffusions on sub‐Riemannian manifolds and some hypocoercive diffusions. As a byproduct, we obtain dimension‐independent reverse Poincaré inequality, reverse logarithmic Sobolev inequality, and gradient bounds on Lie groups with transverse symmetries and for non‐isotropic Heisenberg groups.
Fields of Study & Subjects
Functional Equations Stability Results
Optimization and Variational Analysis
Advanced Optimization Algorithms Research
Publication details
- Journal / source
- Mathematische Nachrichten
- Publisher
- Wiley
- Volume
- 299
- Issue
- 7
- Pages
- 1665–1691
- Publication date
- 23 May 2026
- Language
- EN