Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups

Baudoin, Fabrice; Gordina, Maria; Melcher, Tai

doi:10.1090/s0002-9947-2012-05778-3

Cited by 23 publications

(48 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consequently the sup-normclosability of (E, D) implies lim n E(F − F n ) = 0. Given H ∈ C 1 c (I f,g 0 ) we have in particular 11 lim n N f,g ((F −F n ) 2 , H) = 0 by contractivity and Cauchy-Schwarz. If in addition H(…”

Section: Definitions and Main Resultsmentioning

confidence: 99%

Sup-norm-closable bilinear forms and Lagrangians

Hinz

2015

Annali di Matematica

View full text Add to dashboard Cite

Abstract. We consider symmetric non-negative definite bilinear forms on algebras of bounded real valued functions and investigate closability with respect to the supremum norm. In particular, any Dirichlet form gives rise to a sup-norm closable bilinear form. Under mild conditions a sup-norm closable bilinear form admits finitely additive energy measures. If, in addition, there exists a (countably additive) energy dominant measure, then a sup-norm closable bilinear form can be turned into a Dirichlet form admitting a carré du champ. Moreover, we can always transfer the bilinear form to an isometrically isomorphic algebra of bounded functions on the Gelfand spectrum, where these measures exist. Our results complement a former closability study of Mokobodzki for the locally compact and separable case.

show abstract

Section: Definitions and Main Resultsmentioning

confidence: 99%

Sup-norm-closable bilinear forms and Lagrangians

Hinz

2015

Annali di Matematica

View full text Add to dashboard Cite

show abstract

“…Proof. We shall use the dimension-free Harnack inequality derived in [6] using the generalized curvature condition. Let…”

Section: An Explicit Inverse Poincaré Inequalitymentioning

confidence: 99%

“…for some constants c, c ′ > 0, see also Lemma 4.2 below for a generalized curvature-dimension condition. According to [3] (see also [6,Proposition 4.7]), this implies the following Harnack inequality of type [17] for some constant C > 0:…”

Section: An Explicit Inverse Poincaré Inequalitymentioning

confidence: 99%

Derivative formulas and Poincaré inequality for Kohn-Laplacian type semigroups

Wang

2015

Sci. China Math.

View full text Add to dashboard Cite

As a generalization to the heat semigroup on the Heisenberg group, the diffusion semigroup generated by the subelliptic operator L :for σ an invertible m × m-matrix and {A l } 1≤l≤d some m × m-matrices such that the Hörmander condition holds. We first establish Bismut-type and Driver-type derivative formulae with applications on gradient estimates and the coupling/Liouville properties, which are new even for the heat semigroup on the Heisenberg group; then extend some recent results derived for the heat semigroup on the Heisenberg group.

show abstract

“…[14,15]), quasi-invariance of heat kernel measures in infinite dimensions (e.g. [16,35]), functional inequalities such as Poincaré and log-Sobolev type inequalities (e.g. [13,25,46,56]), and the study of convergence to equilibrium for hypocoercive diffusions (e.g.…”

Section: Introductionmentioning

confidence: 99%