Primitives of volume forms in Carnot groups

2024/10/09 by Annalisa Baldi, Baldi, Annalisa, Bruno Franchi +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2410.06592

openalex publication_date 2024/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the Euclidean space it is known that a function f∈ L² of a ball, with vanishing average,is the divergence of a vector field F∈ L² with‖ F‖_ L²(B) ≤ C ‖f‖_L²(B).In this Note we prove a similar result in any Carnot group \mathbbG for a vanishing average f∈ L^p, 1≤ p < Q, where Q is the so-called homogeneous dimension of \mathbbG.

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