Memoirs of the American Mathematical Society 2013; 65 pp; softcover Volume: 229 ISBN10: 0821891197 ISBN13: 9780821891193 List Price: US$63 Individual Members: US$37.80 Institutional Members: US$50.40 Order Code: MEMO/229/1074
 The authors investigate the global continuity on \(L^p\) spaces with \(p\in [1,\infty]\) of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary nondegeneracy conditions. In this context they prove the optimal global \(L^2\) boundedness result for Fourier integral operators with nondegenerate phase functions and the most general smooth Hörmander class amplitudes i.e. those in \(S^{m} _{\varrho, \delta}\) with \(\varrho , \delta \in [0,1]\). They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted \(L^{p}\) spaces, \(L_{w}^p\) with \(1< p < \infty\) and \(w\in A_{p},\) (i.e. the Muckenhoupt weights) for operators with rough and smooth amplitudes and phase functions satisfying a suitable rank condition. Table of Contents  Prolegomena
 Global boundedness of Fourier integral operators
 Global and local weighted \(L^p\) boundedness of Fourier integral operators
 Applications in harmonic analysis and partial differential equations
 Bibliography
