Abstract:
Let F and F -I be the direct and inverse Fourier transforms in R n . A function u is called a Fourier transform multiplicator from the Lorentz function space Lpr(R n) into the Lorentz space Lq~(R n) if the operator T,(f) = F-~uFf: Ln~(R") ---* Lq,(R") is bounded. Denote by M(Lp~ --, Lq,) the set of all multiphcators from Lp~ in Lq~. This set is a hnear normed space with norm
