\({L^{p}}\) estimates for rough Fourier integral operators

In this paper, we obtain the \({L^p}\) $L^p$ boundedness of Fourier integral operators with rough amplitude \(a \in {L^\infty }S_\rho ^m\) $a\in L^{\infty }{S}_{\rho }^m$ and phase \(\varphi \) $\phi$ that satisfies some generalized derivative estimation and some measure condition. Our main conclusions extend and improve some known results about \({L^p}\) $L^p$ boundedness of Fourier integral operators.