Logarithmic Sobolev inequalities on infinite-dimensional reduced Heisenberg groups

2025/12/03 by Maria Gordina, Gordina, Maria, Liangbing Luo +1
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2512.03349

Abstract

We construct a family of infinite-dimensional reduced Heisenberg groups which can be viewed as infinite-dimensional homogeneous spaces. Such a space is an analogue of finite-dimensional reduced Heisenberg groups in infinite dimensions. We study properties of the hypoelliptic heat kernel measure on this space, including hypoelliptic logarithmic Sobolev inequalities there.

Citations

• Sharp defective log-Sobolev inequalities on H-type groups
• Logarithmic Sobolev inequalities on homogeneous spaces
• Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups
• An application of a functional inequality to quasi-invariance in infinite dimensions
• Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups
• A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups
• Heat kernel analysis on semi-infinite Lie groups
• Square integrable holomorphic functions on infinite-dimensional Heisenberg type groups
• Heat Kernel Analysis on Infinite-Dimensional Heisenberg Groups
• Integrated Harnack inequalities on Lie groups

Related

• Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups
• Logarithmic Sobolev inequalities on homogeneous spaces
• Logarithmic Sobolev, Hardy and Poincaré inequalities on the Heisenberg group
• Heat Kernel Analysis on Infinite-Dimensional Heisenberg Groups
• A simple proof of logarithmic Sobolev inequality on the Heisenberg groups