A remark on the kernel of the CR Paneitz operator. (October 2015)

• Record Type: Journal Article
• Authors: Case, Jeffrey S.; Chanillo, Sagun; Yang, Paul
• Is Part Of: Nonlinear analysis. Volume 126(2015)
• Page Start: 153
• Page End: 158
• Publication Date: 2015-10
• Subjects: CR pluriharmonic functions -- CR Paneitz operator -- Stability; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.04.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: For CR structures in dimension three, the CR pluriharmonic functions are characterized by the vanishing of a third order operator. This third order operator, after composition with the divergence operator, gives the fourth order analogue of the Paneitz operator. In this short note, we give criteria under which the kernel of the CR Paneitz operator contains a supplementary space to the CR pluriharmonic functions.