Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups

On the H.-Q. Li inequality on step-two Carnot groups

“…See Subsection 7.5 for detailed explanation. The idea of this section comes from [13] and we generalize it to a slightly more general setting. To be more precise, we first establish the following lemma.…”

“…Now we are in a position to prove (4). In the following we use µ G t := p G t (g )dg to denote the heat kernel measure on G. Then the second equation of (3), combining with [13,Proposition 2.6] or [7,Theorem 6.15…”

“…Li inequality is preserved under tensorization, some suitable group epimorphism, and the central sum introduced in [21, Section 8.1]. This approach is motivated by the work [13] in which their target is to establish the logarithmic Sobolev inequality w.r.t. the heat kernel measure on nonisotropic Heisenberg groups.…”