Sharp CR Beckner-Onofri inequalities under high-order holomorphic moment constraints

Tuoxin Li; Jingxuan Sun

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arXiv · 2610.31092

Sharp CR Beckner-Onofri inequalities under high-order holomorphic moment constraints

Tuoxin Li·Jingxuan Sun

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Abstract

We establish sharp Beckner--Onofri on the CR sphere $\mathbb{S}^{2N-1}\subset\mathbb C^N$, $N\ge2$, under vanishing holomorphic moments through degree $m\ge1$. The optimal coefficients are $\frac{1}{m+1}$. The function inequality admits a stronger form involving only the energy above degree $m$. We also prove a quantitative concentration estimate in the $1$-Wasserstein distance and show that every maximizing sequence has diverging energy and approaches the family of uniform measures on regular $(m+1)$-polygons. The proof combines subcritical minimization with rigidity of the constrained Euler--Lagrange equation, obtained from an exact radial energy identity and a Hardy space projection estimate. Finally, weighted ball automorphisms yield sharp inequalities without moment constraints, with scalar conformal, barycenter, and holomorphic Gram determinant corrections.

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Tuoxin Li, Jingxuan Sun. 2026-10-22. Sharp CR Beckner-Onofri inequalities under high-order holomorphic moment constraints. https://arxiv.org/abs/2610.31092

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