Abstract
In this paper we construct a fundamental solution for the Laplace operator on the contact complex in Heisenberg groups \({\mathbb H}^{n}\) (Rumin’s complex) relying on the notion of currents in \({\mathbb H}^{n}\) given recently by Franchi, Serapioni and Serra Cassano. This operator is of order 2 on k intrinsic forms for k≠ n, but is of order 4 on n intrinsic forms. As an application, we prove sharp Lp a priori estimates for horizontal derivatives.
Keywords: Heisenberg groups, Differential forms, Currents, Laplace operators, Fundamental solution
Mathematics Subject Classification (2000): 43A80, 58A10, 58A25, 35A08
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baldi, A., Franchi, B. & Tesi, M.C. Fundamental solution and sharp Lp estimates for Laplace operators in the contact complex of Heisenberg groups . Ricerche mat. 55, 119–144 (2006). https://doi.org/10.1007/s11587-006-0009-7
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11587-006-0009-7