ESTIMATES FOR OSCILLATORY INTEGRALS WITH PHASE HAVING D TYPE SINGULARITIES

In this paper, we consider estimates for two-dimensional oscillatory integrals. The phase function of oscillatory integrals is a linear perturbation of a function with D-type singularities. We consider estimates for oscillatory integrals using the maximal functions of the Randol type. Sharp \(L^p_{loc}\) $L_{\mathit{loc}}^p$ estimates for the Randol maximal functions are obtained. Furthermore, we investigate the sharp value of p, depending on whether the phase function has a linearly adapted coordinate system or not.