Primitives of volume forms in Carnot groups
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 \mathbb{G} for a vanishing average f\in L^{p} , 1\le p<Q , where Q is the so-called homogeneous dimension of \mathbb{G} .
Authors
- Bruno Franchi (ORCID: https://orcid.org/0000-0002-6337-956X)
- Annalisa Baldi (ORCID: https://orcid.org/0000-0003-1487-967X)
- Pierre Pansu (ORCID: https://orcid.org/0000-0003-2383-6911)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Paris-Saclay (FR)
- University of Bologna (IT)
Publication Details
- Journal
- Rendiconti Lincei Matematica e Applicazioni
- Published
- 2025-05-06
- DOI
- https://doi.org/10.4171/rlm/1052
- Citations
- 1
- Primary Topic
- Homotopy and Cohomology in Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 3.69