Maximal estimates for an oscillatory operator. (May 2022) - Chen, Jiecheng; Fan, Dashan; Zhao, Fayou
Abstract: Let M be an n -dimensional compact Riemannian manifold. We study an oscillatory operator T α, β, t and obtain its maximal estimate on L p . Particularly, we obtain the sharp estimate on L 1 case. As an application, we obtain the convergence rate of the fractional Schrödinger propagator on the Sobolev space.