H型群上Folland-Stein不等式的极值元与稳定性
Extremals and stability for the Folland-Stein inequality on H-type groups
AI总结：
本文分类了H型群上尖锐$L^2$ Folland-Stein不等式的所有实极值元，证明全局Bianchi-Egnell稳定性估计，给出谱间隙显式界并刻画局部稳定性最优系数，适用于任意正交Clifford模。
AI中文摘要：
我们在H型群上对尖锐的$L^2$ Folland-Stein不等式的所有实值极值元进行了分类，并证明了一个全局的Bianchi-Egnell稳定性估计。在标准泡处的线性化核恰好由其平移和伸缩导数组成。我们还获得了对称模态之上谱间隙的显式界，并刻画了局部稳定性渐近中的最优系数。这些结果适用于任意正交Clifford模。
英文摘要：
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.
