Global L2-boundedness theorems for a class of Fourier integral operators
Analysis of PDEs
2007-05-23 v1 Functional Analysis
Abstract
The local -mapping property of Fourier integral operators has been established in H\"ormander \cite{H} and in Eskin \cite{E}. In this paper, we treat the global -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 Schr\"odinger equations which extends the results of Ben-Artzi and Devinatz \cite{BD}, Walther \cite{Wa}, and \cite{Wa2}.
Keywords
Cite
@article{arxiv.math/0311219,
title = {Global L2-boundedness theorems for a class of Fourier integral operators},
author = {Michael Ruzhansky and Mitsuru Sugimoto},
journal= {arXiv preprint arXiv:math/0311219},
year = {2007}
}