Gagliardo-Nirenberg Inequalities for Differential Forms in Heisenberg Groups
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2015
- DOI:
- 10.48550/arXiv.1506.05904
- arXiv:
- arXiv:1506.05904
- Bibcode:
- 2015arXiv150605904B
- Keywords:
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- Mathematics - Differential Geometry