论文标题
谐波$ NA $组的广义泊松积分的可接受和部门融合
Admissible and sectorial convergence of generalized Poisson integrals on Harmonic $NA$ groups
论文作者
论文摘要
我们证明了FATOU类型的相反的结果，即Lalplace-Beltrami操作员在谐波NA组上的某些本征函数，这些函数与扇形收敛性和复杂度量（签名）测量的Poisson型积分的可接受收敛性有关。该结果扩展了这种结果在经典的上半空间$ \ mathbb {r} _+^{n+1} $的上下文中证明了耳片。在实际双曲空间的退化情况下，也获得了类似的结果。
We prove a converse of Fatou type result for certain eigenfunctions of the Lalplace-Beltrami operator on Harmonic NA groups relating sectorial convergence and admissible convergence of Poisson type integrals of complex (signed) measures. This result extends several results of this kind proved eariler in the context of the classical upper half space $\mathbb{R}_+^{n+1}$. Similar results are also obtained in the degenerate case of the real hyperbolic spaces.
