论文标题
$ \ mathbb {s}^2 $ schr {Ö} schr {Ö}的本地$ l^p $
Local $L^p$ norms of Schr{ö}dinger eigenfunctions on $\mathbb{S}^2$
论文作者
论文摘要
在规范的$ 2 $ -SPHERE上，对于Schr {Ö} Dinger Eigenfunctions，我们获得了一个简单的几何标准，我们可以在一个给定点附近，每一个$ p \ neq 6 $，Sogge的估计。该标准可以根据电势的ra悔转换的临界点来制定，并且与特征函数的选择无关。
On the canonical $2$-sphere and for Schr{ö}dinger eigenfunctions, we obtain a simple geometric criterion on the potential under which we can improve, near a given point and for every $p\neq 6$, Sogge's estimates by a power of the eigenvalue. This criterion can be formulated in terms of the critical points of the Radon transform of the potential and it is independent of the choice of eigenfunctions.
