Semiclassical L^p Estimates of Quasimodes on Submanifolds
arXiv:0905.2240
Abstract
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.
Changes to L^2 norm calculations in Proposition 4.2 (p15-20). No change to main result or general method