Generalized oscillatory integrals and their applications

In this talk we consider the problem of estimation of oscillatory integrals with Mittag–Leffler functions in two variables. The generalisation is that we replace the exponential function with the Mittag–Leffler-type function, to study oscillatory type integrals. Also, it is devoted to the study of estimates of oscillatory integrals and invariant estimates of oscillatory integrals with polynomial phase, summability of oscillatory integrals with phase, which is a polynomial of the third degree of two variables.