Global L-boundedness Theorems for a Class of Fourier Integral Operators

Abstract. The local L-mapping property of Fourier integral operators has been established in Hörmander [14] and in Eskin [12]. In this paper, we treat the global L -boundedness for a class of operators that appears naturally in many problems. As a consequence, we will improve known global results for several classes of pseudodifferential and Fourier integral operators, as well as extend previous results of Asada and Fujiwara [1] or Kumano-go [17]. As an application, we show a global smoothing estimate to generalized Schrödinger equations which extends the results of Ben-Artzi and Devinatz [2], Walther [27], and [28].