$L^p$-bound for the Fourier transform of surface-carried measures supported on hypersurfaces with $D_\infty$ type singularities

Estimate for Fourier transform of surface-carried measures supported on non-convex surfaces of three-dimensional Euclidean space is considered in this paper.The exact convergence exponent was found wherein the Fourier transform of measures is integrable in tree-dimensional space. This result gives an answer to the question posed by Erdösh and Salmhofer.