Results 1 to 10 of about 18 (18)

A Cornucopia of Carnot Groups in Low Dimensions

Analysis and Geometry in Metric Spaces, 2022
Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating.
Le Donne Enrico, Tripaldi Francesca
doaj   +1 more source

Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry

Advanced Nonlinear Studies, 2022
In this article, we establish a Gaffney type inequality, in Wℓ,p{W}^{\ell ,p}-Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind noncompact manifolds)
Baldi Annalisa, Tesi Maria Carla, Tripaldi Francesca   +2 more
doaj   +1 more source

Centered Hardy-Littlewood maximal function on product manifolds

Advances in Nonlinear Analysis, 2022
Let X be the direct product of Xi where Xi is smooth manifold for 1 ≤ i ≤ k. As is known, if every Xi satisfies the doubling volume condition, then the centered Hardy-Littlewood maximal function M on X is weak (1,1) bounded.
Zhao Shiliang
doaj   +1 more source

Commutators on Weighted Morrey Spaces on Spaces of Homogeneous Type

Analysis and Geometry in Metric Spaces, 2020
In this paper, we study the boundedness and compactness of the commutator of Calderón– Zygmund operators T on spaces of homogeneous type (X, d, µ) in the sense of Coifman and Weiss.
Gong Ruming, Li Ji, Pozzi Elodie, Vempati Manasa N.   +3 more
doaj   +1 more source

A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

Analysis and Geometry in Metric Spaces, 2018
Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance.
Le Donne Enrico
doaj   +1 more source

C1,α-rectifiability in low codimension in Heisenberg groups

Analysis and Geometry in Metric Spaces
A natural higher-order notion of C1,α{C}^{1,\alpha }-rectifiability ...
Idu Kennedy Obinna, Maiale Francesco Paolo   +1 more
doaj   +1 more source

On the heat kernel of the Rumin complex and Calderón reproducing formula

Analysis and Geometry in Metric Spaces
We derive several properties of the heat equation with the Hodge operator associated with the Rumin’s complex on Heisenberg groups and prove several properties of the fundamental solution.
Ciatti Paolo, Franchi Bruno, Sire Yannick   +2 more
doaj   +1 more source

Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates

Advanced Nonlinear Studies
On general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using the Rumin complex has been considered in (M. Rumin, “Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie ...
Baldi Annalisa, Tripaldi Francesca
doaj   +1 more source

Polynomial and horizontally polynomial functions on Lie groups. [PDF]

Ann Mat Pura Appl, 2022
Antonelli G, Le Donne E.
europepmc   +1 more source

Counting function estimates for coherent frames and Riesz sequences. [PDF]

Ann Mat Pura Appl
Papageorgiou E, van Velthoven JT.
europepmc   +1 more source