PreprintCC BY 4.0arXiv
A Sharp Sobolev Inequality on Compact CR Manifolds
Abstract
For any n≥ 1, let (M,θ) be a compact strictly pseudoconvex hypersurface type CR manifold with dimension 2n+1, Q=2n+2 be its homogeneous dimension. We prove the sharp Folland--Stein Sobolev inequality on M: if Q*=2Q/(Q−2), then there exists a constant A>0, depending only on (M,θ), such that |u|LQ*(M)2 ≤ K(n)2|∇b u|L2(M)2 + A|u|L2(M)2, u∈ S1,2(M). Here K(n) is the sharp constant in the Folland--Stein Sobolev inequality on the Heisenberg group ℍn.
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BibTeX
@misc{tang2026sharp,
title = {{A Sharp Sobolev Inequality on Compact CR Manifolds}},
author = {Zhongwei Tang and Bingwei Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09841},
eprint = {2609.09841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09841},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Sharp Sobolev Inequality on Compact CR Manifolds
AU - Zhongwei Tang
AU - Bingwei Zhang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.09841
UR - https://arxiv.org/abs/2609.09841
AB - For any n≥ 1, let (M,θ) be a compact strictly pseudoconvex hypersurface type CR manifold with dimension 2n+1, Q=2n+2 be its homogeneous dimension. We prove the sharp Folland--Stein Sobolev inequality on M: if Q^*=2Q/(Q−2), then there exists a constant A>0, depending only on (M,θ), such that |u|_L^Q^*(M)^2 ≤ K(n)^2|∇_b u|_L^2(M)^2 + A|u|_L^2(M)^2, u∈ S^1,2(M). Here K(n) is the sharp constant in the Folland--Stein Sobolev inequality on the Heisenberg group ℍ^n.
ER -