New York Journal of Mathematics
Volume 26 (2020), 261-271


Elena Kim, W. Jacob Ogden, Tommie Reerink, and Yunus E. Zeytuncu

Sobolev and Schatten estimates for the complex Green operator on spheres

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Published: February 20, 2020.
Keywords: Kohn Laplacian, Schatten estimates, Sobolev estimates.
Subject: Primary 32W05; Secondary 32W05.

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 S2n-1 in Cn. We obtain these estimates by using the spectrum of b and the asymptotics of the eigenvalues of the usual Laplace-Beltrami operator.


This work is supported by the NSF (DMS-1659203). The work of the fourth author is also partially supported by a grant from the Simons Foundation (#353525).

Author information

Elena Kim:
Pomona College
Department of Mathematics
610 N College Ave
Claremont, CA 91711, USA


W. Jacob Ogden:
University of Minnesota
School of Mathematics
206 Church Street SE
Minneapolis, MN, 55455, USA


Tommie Reerink:
Massachusetts Institute of Technology
Green Hall, 350 Memorial Drive
Cambridge, MA 02139, USA


Yunus E. Zeytuncu:
University of Michigan--Dearborn
Department of Mathematics and Statistics
2048 Evergreen Road
Dearborn, MI 48128, USA