Maximal estimates for an oscillatory operator. (May 2022)

• Record Type: Journal Article
• Authors: Chen, Jiecheng; Fan, Dashan; Zhao, Fayou
• Is Part Of: Nonlinear analysis. Volume 218(2022)
• Publication Date: 2022-05
• Subjects: 41A25 -- 42B20; Compact Riemannian manifold -- Convergence rate -- Fractional Schrödinger propagator; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112792
• Languages: English
• ISSNs: 0362-546X

Abstract

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.