1Department of Mathematics, Ghent University, Belgium 2Department of Mathematics, University of Bologna, Italy 3Institut de Mathématiques, UMR5219, CNRS, Université de Toulouse, France
Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 629-650
We give a sufficient condition under which the global Poincaré inequality on Carnot groups holds true for a large family of probability measures absolutely continuous with respect to the Lebesgue measure. Additionally, we show that the global Poincaré inequality holds true on any Carnot group for a certain choice of a probability measure adapted to the structure of each Carnot group, and whose formula is explicitly given. Consequently, we extend the results of a previous work by the authors [q-Poincaré inequalities on Carnot groups with a filiform Lie algebra, Potential Analysis 60/3 (2024) 1067--1092] targeted on filiform Carnot groups to any Carnot group. As a result, the Schrödinger operators associated with the density of the considered probability measure have a spectral gap.
1
Department of Mathematics, Ghent University, Belgium
2
Department of Mathematics, University of Bologna, Italy
3
Institut de Mathématiques, UMR5219, CNRS, Université de Toulouse, France
Marianna Chatzakou; Serena Federico; Boguslaw Zegarlinski. Poincaré Inequalities on Carnot Groups and Spectral Gap of Schrödinger Operators. Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 629-650. http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a9/
@article{JOLT_2025_35_3_a9,
author = {Marianna Chatzakou and Serena Federico and Boguslaw Zegarlinski},
title = {Poincar\'e {Inequalities} on {Carnot} {Groups} and {Spectral} {Gap} of {Schr\"odinger} {Operators}},
journal = {Journal of Lie Theory},
pages = {629--650},
year = {2025},
volume = {35},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a9/}
}
TY - JOUR
AU - Marianna Chatzakou
AU - Serena Federico
AU - Boguslaw Zegarlinski
TI - Poincaré Inequalities on Carnot Groups and Spectral Gap of Schrödinger Operators
JO - Journal of Lie Theory
PY - 2025
SP - 629
EP - 650
VL - 35
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a9/
ID - JOLT_2025_35_3_a9
ER -
%0 Journal Article
%A Marianna Chatzakou
%A Serena Federico
%A Boguslaw Zegarlinski
%T Poincaré Inequalities on Carnot Groups and Spectral Gap of Schrödinger Operators
%J Journal of Lie Theory
%D 2025
%P 629-650
%V 35
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a9/
%F JOLT_2025_35_3_a9
