On Lp-boundedness of Fourier Integral Operators

In this paper, we get an Lp boundedness of Fourier integral operators with rough amplitude a∈L∞Sϱm,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a\in L^{\infty } S^{m}_{\varrho },~$\end{document} and phase φ∈L∞Φ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varphi \in L^{\infty }{\Phi }^{2}$\end{document} for 1≤p≤+∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1\leq p\leq +\infty $\end{document}. This is an improvement of the corresponding results in Dos Santos Ferreira and Staubach (Mem. Amer. Math. Soc. 229, 1074, 2014).