On estimates for convolution operators related to exceptional surfaces

In this talk, we will discuss convolution operators with oscillatory kernels, which are related to solutions of the Cauchy problem for strictly hyperbolic equations. The operator is associated with the characteristic hypersurfaces of a hyperbolic equation and a smooth amplitude function that is homogeneous for large values of the argument. We will consider convolution operators assuming that the corresponding hypersurface belongs to an exceptional class of surfaces.