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Extremals and stability for the Folland-Stein inequality on H-type groups
Abstract
We classify all real extremals of the sharp L2 Folland-Stein inequality on H-type groups and prove a global Bianchi-Egnell stability estimate. The linearized kernel at the standard bubble consists exactly of its translation and dilation derivatives. We also obtain explicit bounds for the spectral gap above the symmetry modes and characterize the optimal coefficient in the local stability asymptotics. The results apply to arbitrary orthogonal Clifford modules.
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BibTeX
@misc{yang2026extremals,
title = {{Extremals and stability for the Folland-Stein inequality on H-type groups}},
author = {Zhipeng Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30531},
eprint = {2609.30531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30531},
}
RIS
TY - UNPB
TI - Extremals and stability for the Folland-Stein inequality on H-type groups
AU - Zhipeng Yang
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30531
UR - https://arxiv.org/abs/2609.30531
AB - We classify all real extremals of the sharp L^2 Folland-Stein inequality on H-type groups and prove a global Bianchi-Egnell stability estimate. The linearized kernel at the standard bubble consists exactly of its translation and dilation derivatives. We also obtain explicit bounds for the spectral gap above the symmetry modes and characterize the optimal coefficient in the local stability asymptotics. The results apply to arbitrary orthogonal Clifford modules.
ER -