Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg

Li, Hongquan

doi:10.1016/j.jfa.2006.02.016

Cited by 82 publications

(107 citation statements)

References 22 publications

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“…[16]) or certain smoothing properties of the semigroup (see e.g. [5], [17], [36], [6], [27] and references therein). Even in the case of diffusion operators in finite dimensions it is a hard problem for which a relatively satisfactory solution currently only exists in case of (products of) Heisenberg type groups; for q = 1 2 the other groups constitute a formidable challenge.…”

Section: Generalised Gradient Boundsmentioning

confidence: 99%

Linear and Nonlinear Dissipative Dynamics

Zegarliński

2016

Reports on Mathematical Physics

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Section: Generalised Gradient Boundsmentioning

confidence: 99%

Linear and Nonlinear Dissipative Dynamics

Zegarliński

2016

Reports on Mathematical Physics

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“…Connections between the probabilistic behaviour of subelliptic diffusions and analytic properties of the corresponding heat semigroups, most directly expressed in functional inequalities, have attracted a lot of attention [17,48,43,3]. For instance, denoting by P t f the (minimal) heat semigroup generated by…”

Section: Future Prospectsmentioning

confidence: 99%

Geometry of subelliptic diffusions

Thalmaier

2016

EMS Series of Lectures in Mathematics

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Abstract. These lectures focus on some probabilistic aspects related to subRiemannian geometry. The main intention is to give an introduction to hypoelliptic and subelliptic diffusions. The notes are written from a geometric point of view trying to minimize the weight of "probabilistic baggage" necessary to follow the arguments. We discuss in particular the following topics: stochastic flows to second order differential operators; smoothness of transition probabilities under Hörmander's brackets condition; control theory and Stroock-Varadhan's support theorems; Malliavin calculus; Hörmander's theorem. The notes start from well-known facts in Geometric Stochastic Analysis and guide to recent on-going research topics, like hypoelliptic heat kernel estimates; gradient estimates and Harnack type inequalities for subelliptic diffusion semigroups; notions of curvature related to sub-Riemannian diffusions.

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“…[27] and references therein). More recently such bounds where sharpened, ( [4], [23], [13]), with the same Gaussian factor on both sides of the sandwich. As a consequence it was possible to prove the following gradient bounds…”

Section: Analysis On Heisenberg Groupmentioning

confidence: 99%

Analysis on Extended Heisenberg Group

Zegarliński¹

2011

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg

Cited by 82 publications

References 22 publications

Linear and Nonlinear Dissipative Dynamics

Linear and Nonlinear Dissipative Dynamics

Geometry of subelliptic diffusions

Analysis on Extended Heisenberg Group

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