Endpoint resolvent estimates for compact Riemannian manifolds
Endpoint resolvent estimates for compact Riemannian manifolds
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紧凑黎曼流形的端点解析估计
DOI：
10.1016/j.jfa.2016.11.012
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发表时间：
2016
影响因子：
1.7
通讯作者：
L. Schimmer
中科院分区：
文献类型：
--
作者：
R. Frank;L. Schimmer
在端点p= 2 (n+ 1)/(n+ 3)的情况下，证明了n维紧黎曼流形上Laplace-Beltrami算子解的L p→L p的界。由于Kenig-Ruiz-Sogge，如果移除正半线的抛物线邻域，则它对光谱参数z的行为与欧几里得类似物相同。这个区域是最优的，例如，在球的情况下。
We prove L p→ L p′ bounds for the resolvent of the Laplace–Beltrami operator on a compact Riemannian manifold of dimension n in the endpoint case p= 2 (n+ 1)/(n+ 3). It has the same behavior with respect to the spectral parameter z as its Euclidean analogue, due to Kenig–Ruiz–Sogge, provided a parabolic neighborhood of the positive half-line is removed. This is region is optimal, for instance, in the case of a sphere.