Article ID Journal Published Year Pages File Type
4590241 Journal of Functional Analysis 2014 32 Pages PDF
Abstract

We prove families of uniform (Lr,Ls)(Lr,Ls) 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 [7]. 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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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