Chuanwei Gao, Changxing Miao, Jianwei-Urbain Yang
Published 2019-01-06Version 1
We establish certain square function estimates for a class of oscillatory integral operators with homogeneous phase functions. These results are employed to deduce a refinement of a previous result of Mockenhaupt Seeger and Sogge \cite{MSS-jams} on the local smoothing property for Fourier integral operators, which arise naturally in the study of wave equations on compact Riemannian manifolds. The proof is an adaptation of the bilinear approach of Tao and Vargas \cite{Tao-Vargas-II}, %as well as Garrig\'os and Seeger \cite{GaSe09}, and based on bilinear oscillatory integral estimates of Lee \cite{Lee-JFA}.
Nuclearity, Schatten-von Neumann classes, distribution of eigenvalues and $L^p$-$L^q$-boundedness of Fourier integral operators on compact manifolds
$L\sp p$-$L\sp q$ regularity of Fourier integral operators with caustics
Boundedness of Fourier integral operators on classical function spaces
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