Strichartz estimates on asymptotically hyperbolic manifolds

Abstract

We prove local in time Strichartz estimates without loss for the restriction of the solution of the Schrödinger equation, outside a large compact set, on a class of asymptotically hyperbolic manifolds.

Semi-classical functional calculus on manifolds with ends and weighted L^p estimates

“…We also derive certain weighted L p → L p boundedness properties of such operators. Further applications to Littlewood-Paley decompositions [5] and Strichartz estimates [4] will be published separately. Needless to say, the range of applications of the present functional calculus goes beyond Strichartz estimates; there are many problems which naturally involve spectral cutoffs at high frequencies in linear and non linear PDEs (LittlewoodPaley decompositions, paraproducts) or in spectral theory (trace formulas).…”

Strichartz estimates for convex co-compact hyperbolic surfaces

“…These are obtained by a direct self-contained argument. We remark however that the results of Bouclet [Bou2] give stronger estimates which could be used in case no-loss estimates are obtained in the compact part.…”

Sharp Low Frequency Resolvent Estimates on Asymptotically Conical Manifolds

“…We next consider Strichartz estimates, which is the main original motivation of this paper. The related results will appear in a forthcoming paper [7] but we explain below why Theorems 1.1 and 1.2 are relevant to handle the contribution of low frequencies. In particular, we will see where using the weight r −1 is crucial.…”