Weighted Sobolev L 2 Estimates for a Class of Fourier Integral Operators

In this paper we develop elements of the global calculus of Fourier integral operators in R n under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L 2 estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As… (More)