Sharp Moser-Onofri inequality on the CR sphere under zero-moment constraints and its application to the stability of the CR Moser-Onofri inequality

Lu Chen; Guozhen Lu

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arXiv · 2610.29877

Sharp Moser-Onofri inequality on the CR sphere under zero-moment constraints and its application to the stability of the CR Moser-Onofri inequality

Lu Chen·Guozhen Lu

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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.

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Lu Chen, Guozhen Lu. 2026-10-21. Sharp Moser-Onofri inequality on the CR sphere under zero-moment constraints and its application to the stability of the CR Moser-Onofri inequality. https://arxiv.org/abs/2610.29877

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