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Morrey–Campanato functional spaces for Carnot groups
Banach Journal of Mathematical Analysis, 2023We shortly review the historical path of Morrey–Campanato functional spaces and the fundamentals of Carnot groups. Then, we merge these two topics, by recovering several classical results concerning regularity of Morrey–Campanato spaces in the framework ...
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A coupling strategy for Brownian motions at fixed time on Carnot groups using Legendre expansion
Electronic Journal of ProbabilityWe propose a new simple construction of a coupling at a fixed time of two sub-Riemannian Brownian motions on the Heisenberg group and on the free step 2 Carnot groups.
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Non co-adapted couplings of Brownian motions on free, step 2 Carnot groups
E S A I M: Probability & StatisticsOn the free, step $2$ Carnot groups of rank $n$ $\Ge_n$, the subRiemannian Brownian motion consists in a $\mathbb{R}^n$-Brownian motion together with its $\frac{n(n-1)}{2}$ Lévy areas.
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For a 2-step Carnot group D_n, "dim" D_n=n+1, with horizontal distribution of corank 1, we proved that the minimal number N_(X_(D_n ) ) such that any two points u,v∈D_n can be joined by some basis horizontal k-broken line (i.e.
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On Gradient Estimates of the Heat Semigroups on Step-Two Carnot Groups
Potential AnalysisIn this work, we give a sufficient condition for a step-two Carnot group to satisfy the quasi Bakry-\'Emery curvature condition. As an application, we establish the gradient estimate for the heat semigroup on the free step-two Carnot group with three ...
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