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

Abstract

The local $L^2$-mapping property of Fourier integral operators has been established in Hörmander \cite{H} and in Eskin \cite{E}. In this paper, we treat the global $L^2$-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 pseudo-differential and Fourier integral operators, as well as extend previous results of Asada and Fujiwara \cite{AF} or Kumano-go \cite{Ku}. As an application, we show a global smoothing estimate to generalized Schrödinger equations which extends the results of Ben-Artzi and Devinatz \cite{BD}, Walther \cite{Wa}, and \cite{Wa2}.

Cited by in corpus (7)

• On Hadamard's global inverse function theorem (On global inversion of homogeneous maps)
• Calculus, continuity and global wave-front properties for Fourier integral operators on ${\mathbf{R}}^d$
• Schrödinger type propagators, pseudodifferential operators and modulation spaces
• Sharp $L^p$ estimates for Schrödinger groups
• Fourier integral operators algebra and fundamental solutions to hyperbolic systems with polynomially bounded coefficients on R^n
• Pseudo-differential operators with nonlinear quantizing functions
• A family of anisotropic integral operators and behaviour of its maximal eigenvalue