Gagliardo-Nirenberg Inequalities for Differential Forms in Heisenberg Groups

2015/06/19 by Annalisa Baldi, Baldi, Annalisa, Bruno Franchi +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1506.05904

arxiv created 2015/06/19 · arxiv updated 2015/06/22

Abstract

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 δu (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.

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