Gagliardo-Nirenberg Inequalities for Differential Forms in Heisenberg Groups
Differential Geometry
2015-06-22 v1
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 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.
Keywords
Cite
@article{arxiv.1506.05904,
title = {Gagliardo-Nirenberg Inequalities for Differential Forms in Heisenberg Groups},
author = {Annalisa Baldi and Bruno Franchi and Pierre Pansu},
journal= {arXiv preprint arXiv:1506.05904},
year = {2015}
}