Tauberian theorems for generalized funtions

Tauberian theorems are usually assumed to connect the asymptotic behavior of a generalized function (or a distribution) at infinity with the asymptotic behavior in the neighborhood of zero of its integral transform (Fourier, Laplace, etc). In this talk, we consider a multidimensional generalization of Hardy–Littlewood, Keldysh and Wiener theorems.