Zobrazeno 1 - 10
of 95
pro vyhledávání: '"Baldi Annalisa"'
Publikováno v:
Advanced Nonlinear Studies, Vol 22, Iss 1, Pp 484-516 (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 man
Externí odkaz:
https://doaj.org/article/a3c9a226ce784352b0400cb828da5bd6
The aim of this paper is to study a Laplace-type operator and its fundamental solution on the characteristic plane in the Heisenberg group $\mathbb{H}^2$. We introduce a conformal version of the Laplacian and we prove that the distance induced by the
Externí odkaz:
http://arxiv.org/abs/2410.23256
In the Euclidean space it is known that a function $f\in L^2$ of a ball, with vanishing average,is the divergence of a vector field $F\in L^2$ with$$\| F\|\_{ L^2(B)} \le C \|f\|\_{L^2(B)}.$$In this Note we prove a similar result in any Carnot group
Externí odkaz:
http://arxiv.org/abs/2410.06592
Autor:
Baldi, Annalisa, Tripaldi, Francesca
On general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using the Rumin complex has been considered by Rumin, who introduced a 0-order pseudodifferential operator on forms. However, for questions regarding regular
Externí odkaz:
http://arxiv.org/abs/2407.14316
It is shown that higher degree exact differential forms on compact Riemannian $n$-manifolds possess continuous primitives whose uniform norm is controlled by their $L^n$ norm. A contact sub-Riemannian analogue is proven, with differential forms repla
Externí odkaz:
http://arxiv.org/abs/2403.16602
We define a BV -type space in the setting of Carnot groups (i.e., simply connected Lie groups with stratified nilpotent Lie algebra) that allows one to characterize all distributions F for which there exists a continuous horizontal vector field {\Phi
Externí odkaz:
http://arxiv.org/abs/2210.15490
In the last few years the authors proved Poincar\'e and Sobolev type inequalities in Heisenberg groups $\mathbb{H}^n$ for differential forms in the Rumin's complex. The need to substitute the usual de Rham complex of differential forms for Euclidean
Externí odkaz:
http://arxiv.org/abs/2103.02308
Publikováno v:
In Journal of Functional Analysis 15 July 2023 285(2)
In this paper, we prove Poincar\'e and Sobolev inequalities for differential forms in $L^1(\mathbb R^n)$. The singular integral estimates that it is possible to use for $L^p$, $p>1$, are replaced here with inequalities which go back to Bourgain-Brezi
Externí odkaz:
http://arxiv.org/abs/1902.10138
In this paper, we prove interior Poincar{\'e} and Sobolev inequalities in Euclidean spaces and in Heisenberg groups, in the limiting case where the exterior (resp. Rumin) differential of a differential form is measured in L 1 norm. Unlike for L p , p
Externí odkaz:
http://arxiv.org/abs/1902.04819