Logarithmic Sobolev inequalities on infinite-dimensional reduced Heisenberg groups

TL;DR

This paper constructs infinite-dimensional reduced Heisenberg groups as homogeneous spaces and investigates their hypoelliptic heat kernel measures, establishing logarithmic Sobolev inequalities in this infinite-dimensional setting.

Contribution

It introduces a novel class of infinite-dimensional homogeneous spaces and proves hypoelliptic logarithmic Sobolev inequalities on them, extending finite-dimensional results.

Findings

Established hypoelliptic logarithmic Sobolev inequalities on infinite-dimensional reduced Heisenberg groups

Constructed a new family of infinite-dimensional homogeneous spaces analogous to finite-dimensional groups

Analyzed properties of the hypoelliptic heat kernel measure in infinite dimensions

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.