On \(L^p\) boundedness of rough Fourier integral operators (Q6612617)

In this paper, the authors study the \(L^p\)-boundedness of a class of rough Fourier integral operators \(T_{a,\varphi}\) with amplitude \(a(x, \xi)\in L^{\infty}S^m_{\rho}\) and phase function \(\varphi(x,\xi)\in L^{\infty}\Phi^2\) which satisfies a measure condition. Under some suitable admissible conditions on \(p\) which depends on \(m\), \(\rho \) and \(n\), they prove that \(T_{a,\varphi}\) is bounded on \(L^p\). The main results extend and improve some known results about \(L^p\) boundedness of Fourier integral operators.