Restriction results for multilinear multipliers in weighted settings

Abstract

We obtain restriction results of de Leeuw’s type for maximal operators defined through multilinear Fourier multipliers of either strong or weak type acting on weighted Lebesgue spaces. We give some applications of our development. In particular, we obtain periodic weighted results for Coifman–Meyer-, Hörmander- and Hörmander–Mihlin-type multilinear multipliers.