Hypoelliptic heat kernel inequalities on the Heisenberg group

By B. Driver, T. Melcher. 2005

96 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/58f97ece325e44994dab61ab71f2a8824c6d7313

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Gradient estimates for heat kernels and harmonic functions (2017, background): “On Heisenberg type groups, Driver and Melcher [38] and Hu and Li [67] obtained a Bakry-Émery type inequality, which implies (GLY∞).”
Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality (2011, background): “d fails to hold even for simple subelliptic diﬀusion operators like the sub-Laplacian on the Heisenberg group (see [J]). However in the past few years, numerous works like [BBBC], [BBBQ], [BB], [Bo], [DM], [E], [IKZ], [Li] and [Q] have shown on some examples that the heat semigroup associated with c”
The subelliptic heat kernel on SU(2): representations, asymptotics and gradient bounds (2008, background): “On the other hand, recent works have started to study gradient estimates for subelliptic semigroups (see for instance [5], [12], [19], [22]).”
Duality on gradient estimates and Wasserstein controls (2009, background): “As observed in [12], we cannot expect such a multiplicativity in the case of Example 4.”
Precise estimates for the subelliptic heat kernel on H-type groups (2008, methodology): “nt under this denition. The main theorem of this article is the following: Theorem 2.4. There exists a nite constant Ksuch that for all f2C, jrP tfjKP t(jrfj): (2.12) Following an argument found in [5], by left-invariance of P t and r, we see that in order to establish (2.12) it suces to show that i”
Coercive Inequalities on Metric Measure Spaces (2009, methodology): “As an application of our technique we also prove (see Section 6-7) the LogSobolev inequality for the heat kernel measure on the Heisenberg group, (a topic which attracted recently some extra attention [32], [17]).”
Riesz transform on manifolds and heat kernel regularity (2004, unknown): “(1.12) (Added after acceptation: we mention a paper by Driver and Melcher [31] where theLp versions of such inequalities (withc = 1) are proved on the Heisenberg groupH1 for all p > 1 by probabilistic methods.)”