Sharp global bounds for the Hessian on pseudo-Hermitian manifolds. (English) Zbl 1205.32027
Cabrelli, Carlos (ed.) et al., Recent developments in real and harmonic analysis. In honor of Carlos Segovia. Boston, MA: Birkhäuser (ISBN 978-0-8176-4531-1/hbk; 978-0-8176-4588-5/ebook). Applied and Numerical Harmonic Analysis, 159-172 (2010).
The authors consider an abstract CR manifold of hypersurface type, strictly pseudoconvex and equipped with a pseudo-Hermitian metric. After defining the natural sub-Laplacian operator, they use the Bochner identities to prove Cordes-Friedrichs type inequalities for the Hessian of a real valued function. As an application, they prove a regularity result for \(p\)-harmonic functions on the Heisenberg group.
For the entire collection see [Zbl 1182.42001].
For the entire collection see [Zbl 1182.42001].
Reviewer: Mauro Nacinovich (Roma)
MSC:
| 32V20 | Analysis on CR manifolds |
| 58E20 | Harmonic maps, etc. |
| 53A55 | Differential invariants (local theory), geometric objects |
