Sharp Moser-Onofri inequality on the CR sphere under zero-moment constraints and its application to the stability of the CR Moser-Onofri inequality
Year: 2026
Type: preprint
Abstract: In this paper, we establish the sharp Moser--Onofri inequality in CR sphere under zero-moment constraints. By combining a decomposition into low and high spherical harmonics with the known CR localization estimates, we first prove the existence of extremals of the subcritical Moser--Onofri inequality under zero-moment constraints. We then derive their Euler--Lagrange equation, establish their smoothness, and eliminate the moment multiplier by means of the infinitesimal CR conformal action. Using the summation identity (4.9) on the Hardy space $H^2(B^n)$, we show that the extremals of subcritical Moser-Onofri inequality in CR sphere under zero-moment constraints are constants. By a limiting argument, we deduce the sharp Moser--Onofri inequality in CR sphere under zero-moment constraints. As an application, we establish the stability of Moser--Onofri inequality in CR sphere with the best stability constant.
Source: arXiv (Cornell University)
Authors: Chen, Lu, Lu, Guozhen
Institutions: Beijing Institute of Technology, University of Connecticut
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223210807