Global L2-boundedness theorems for a class of Fourier integral operators

The local L-2-mapping property of Fourier integral operators has been established in Hormander (1971) and in Eskin (1970). In this article, we treat the global L-2-boundedness for a class of operators that appears naturally in many problems. As a consequence, we improve known global results for several classes of pseudodifferential and Fourier integral operators, as well as extend previous results of Asada and Fujiwara (1978) or Kumano-go (1976). As an application, we show a global smoothing estimate for generalized Schrodinger equations which extends the results of Ben-Artzi and Devinatz (1991) and Walther (1999); (2002).