The L 1-Sobolev inequality states that the L n/(n--1)-norm of a compactly
supported function on Euclidean n-space is controlled by the L 1-norm of its
gradient. The generalization to differential forms (due to Lanzani & Stein and
Bourgain & Brezis) is recent, and states that a the L n/(n--1)-norm of a
compactly supported differential h-form is controlled by the L 1-norm of its
exterior differential du and its exterior codifferential $\delta$u (in special
cases the L 1-norm must be replaced by the H 1-Hardy norm). We shall extend
this result to Heisenberg groups in the framework of an appropriate complex of
differential forms

Baldi, Annalisa

Franchi, Bruno

Pansu, Pierre

Mathematische Annalen

English

arXiv

The $L^1$-Sobolev inequality  states that for compactly supported functions $u$ on the Euclidean $n$-space, 
the $L^{n/(n-1)}$-norm of a compactly supported function
 is controlled by the $L^1$-norm of its gradient.
The generalization to differential forms (due to Lanzani &amp; Stein and Bourgain &amp; Brezis) is recent, and states that a the $L^{n/(n-1)}$-norm of a compactly supported differential
$h$-form is controlled by the $L^1$-norm of its exterior differential $du$ and its exterior codifferential $delta u$ (in special cases the 
$L^1$-norm must be replaced by the $mc H^1$-Hardy norm).  We shall extend this result to Heisenberg groups in the framework of an appropriate complex of differential forms

Gagliardo-Nirenberg Inequalities for Differential Forms in Heisenberg Groups

Abstract

Similar works

Full text

Available Versions

Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna

Crossref