Coxeter平面系是$\mathbb C^n$上扭球平均的内射集
Coxeter system of planes are sets of injectivity for the twisted spherical means on $\mathbb C^n$
摘要：
本文证明了任意一对垂直平面都是$L^p(\mathbb C^n) (n\geq2)$的扭球平均的内射集，并证明了$1\leq p\leq2.$对任意偶数个平面的Coxeter系统都是$L^p(\mathbb C^n).$的扭球平均的内射集。进一步证明了集合$S_R^{2n-1}\times\mathbb C$是$\mathbb C^{n+1}.$上某类函数的扭球平均的内射集
英文摘要：
In this article, we prove that any pair of perpendicular planes is a set of injectivity for the twisted spherical means (TSM) for $L^p(\mathbb C^n) (n\geq2)$ with $1\leq p\leq2.$ Then, we imitate that any Coxeter system of even number of planes is a set of injectivity for the TSM for $L^p(\mathbb C^n).$ We further observe that a set $S_R^{2n-1}\times\mathbb C$ is a set of injectivity for the TSM for a ceratin class of functions on $\mathbb C^{n+1}.$
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