Improved variable coefficient square functions and local smoothing of Fourier integral operators
Abstract
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 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 Tao-Vargas-II, %as well as Garrig\'os and Seeger GaSe09, and based on bilinear oscillatory integral estimates of Lee Lee-JFA.
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