Semiclassical L^p Estimates of Quasimodes on Submanifolds

Details Semiclassical L^p Estimates of Quasimodes on Submanifolds Semiclassical L^p Estimates of Quasimodes on Submanifolds

2009-05-14

arxiv.org/abs/0905.2240v2

Mathematics

Analysis of PDEs

Changes to L^2 norm calculations in Proposition 4.2 (p15-20). No change to main result or general method

Scientific paper

Let M be a compact manifold and P = P(h) a semiclassical pseudodifferential operator on M . Suppose that u(h) is a L^2 normalised family of functions such that P(h)u(h) is O(h) in L^2, as h goes to 0. Then, for any compact submanifold Y contained in M, we obtain estimates on the L^p norm of u(h) restricted to Y, with exponents that are sharp for h goes to 0. As part of the technical development we prove some extensions of the abstract Strichartz estimates of Keel and Tao.

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