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arXiv · 1506.05904

Gagliardo-Nirenberg Inequalities for Differential Forms in Heisenberg Groups

Annalisa Baldi·Bruno Franchi·Pierre Pansu
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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 $\delta$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.

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Annalisa Baldi, Bruno Franchi, Pierre Pansu. 2015-06-19. Gagliardo-Nirenberg Inequalities for Differential Forms in Heisenberg Groups. https://arxiv.org/abs/1506.05904

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