Homogeneous Estimates for Oscillatory Integrals.

摘要

Let u(x,t) be the solution to the free time-dependent Schrodinger equation at the point (x,t) in space-time Rn+1 with initial data f. We characterize the size of u in terms Lp (Lq)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces Hs (Rn). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interpolation of vector valued weighted Lebesgue spaces.