Article ID Journal Published Year Pages File Type
5772251 Journal of Functional Analysis 2017 15 Pages PDF
Abstract
We prove Lp→Lp′ 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.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
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