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

Abstract

We establish sharp Beckner--Onofri on the CR sphere 𝕊^2N−1⊂ℂ^N, N≥2, under vanishing holomorphic moments through degree m≥1. The optimal coefficients are 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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BibTeX RIS

BibTeX

@misc{li2026sharp,
  title = {{Sharp CR Beckner-Onofri inequalities under high-order holomorphic moment constraints}},
  author = {Tuoxin Li and Jingxuan Sun},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31092},
  eprint = {2610.31092},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31092},
}

RIS

TY  - UNPB
TI  - Sharp CR Beckner-Onofri inequalities under high-order holomorphic moment constraints
AU  - Tuoxin Li
AU  - Jingxuan Sun
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31092
UR  - https://arxiv.org/abs/2610.31092
AB  - We establish sharp Beckner--Onofri on the CR sphere 𝕊^2N−1⊂ℂ^N, N≥2, under vanishing holomorphic moments through degree m≥1. The optimal coefficients are 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.
ER  -

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