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arXiv · 1406.1940

Concerning $L^p$ resolvent estimates for simply connected manifolds of constant curvature

Shanlin Huang·Christopher D. Sogge
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Abstract

We prove families of uniform $(L^r,L^s)$ resolvent estimates for simply connected manifolds of constant curvature (negative or positive) that imply the earlier ones for Euclidean space of Kenig, Ruiz and the second author \cite{KRS}. In the case of the sphere we take advantage of the fact that the half-wave group of the natural shifted Laplacian is periodic. In the case of hyperbolic space, the key ingredient is a natural variant of the Stein-Tomas restriction theorem.

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Shanlin Huang, Christopher D. Sogge. 2014-06-08. Concerning $L^p$ resolvent estimates for simply connected manifolds of constant curvature. https://arxiv.org/abs/1406.1940

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