Work

Primitives of volume forms in Carnot groups

Year: 2025

Type: article

Abstract: 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 , where Q is the so-called homogeneous dimension of \mathbb{G} .

Source: Rendiconti Lincei Matematica e Applicazioni

DOI: 10.4171/rlm/1052

Authors: Annalisa Baldi, Bruno Franchi, Pierre Pansu

Institutions: University of Bologna, Centre National de la Recherche Scientifique, Université Paris-Saclay

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Agence Nationale de la Recherche, Università di Bologna

Awards: Groups acting on fractals, G5245466801