调和$NA$群上广义Poisson积分的容许收敛和扇形收敛
Admissible and sectorial convergence of generalized Poisson integrals on Harmonic $NA$ groups
摘要：
证明了调和NA群上的Lalplace-Beltrami算子的某些特征函数的Fatou型结果的逆，这些特征函数与复（符号）测度的Poisson型积分的扇形收敛和容许收敛有关.这个结果推广了在经典上半空间$\mathbb{R}_+^{n+1}$中较早证明的几个这类结果。在实双曲空间的退化情形下也得到了类似的结果。
英文摘要：
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.
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