Inequalities of Hardy-Sobolev type in Carnot-Carathéodory spaces
| dc.creator | Danielli, Donatella | |
| dc.creator | Garofalo, Nicola | |
| dc.creator | Phuc, Nguyen Cong | |
| dc.date | 2008-04-17 | |
| dc.date.accessioned | 2026-07-07T09:33:12Z | |
| dc.date.available | 2026-07-07T09:33:12Z | |
| dc.description | We consider various types of Hardy-Sobolev inequalities on a Carnot-Carathéodory space $(\Om, d)$ associated to a system of smooth vector fields $X=\{X_1, X_2,...,X_m\}$ on $\RR^n$ satisfying the Hörmander's finite rank condition $rank Lie[X_1,...,X_m] \equiv n$. One of our main concerns is the trace inequality \int_{\Om}|ϕ(x)|^{p}V(x)dx\leq C\int_{\Om}|Xϕ|^{p}dx,\qquad ϕ\in C^{\infty}_{0}(\Om), where $V$ is a general weight, i.e., a nonnegative locally integrable function on $\Om$, and $1<p<+\infty$. Under sharp geometric assumptions on the domain $\Om\subset \Rn$ that can be measured equivalently in terms of subelliptic capacities or Hausdorff contents, we establish various forms of Hardy-Sobolev type inequalities. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/0804.2833 | |
| dc.identifier | http://arxiv.org/abs/0804.2833 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159051 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35H20 ; 26D10 | |
| dc.title | Inequalities of Hardy-Sobolev type in Carnot-Carathéodory spaces | |
| dc.type | text |