Sobolev and Schatten estimates for the complex Green operator on spheres.
- Resource Type
- Article
- Authors
- Kim, Elena; Ogden, W. Jacob; Reerink, Tommie; Zeytuncu, Yunus E.
- Source
- New York Journal of Mathematics. 2020, p261-271. 11p.
- Subject
- *SPHERES
*ESTIMATES
*EIGENVALUES
- Language
- ISSN
- 1076-9803
The complex Green operator G on CR manifolds is the inverse of the Kohn-Laplacian □b on the orthogonal complement of its kernel. In this note, we prove Schatten and Sobolev estimates for G on the unit sphere 핊2n-1 ⊂ ℂn. We obtain these estimates by using the spectrum of □b and the asymptotics of the eigenvalues of the usual Laplace-Beltrami operator. [ABSTRACT FROM AUTHOR]