$$L^{1}$$-boundedness of rough Fourier integral operators

In this paper, we study the $$L^{1}$$ boundedness of Fourier integral operator $$T_{\phi ,a}$$ with rough symbol $$a\in L^{\infty }S^{m}_{\rho }$$ and a new class phase $$\phi $$ . class, extend $$L^{\infty }\Phi ^{2}$$ non-degeneracy conditions to some generalized derivative estimation measure condition respectively. Our main result substantially extends improves known results about operator. Moreover, in paper can be used prove maximal wave