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

Abstract

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