On restriction of maximal multipliers in weighted settings

Abstract

We obtain restriction results of K. De Leeuw's type for maximal operators defined through Fourier multipliers of either strong or weak type for weighted $ L^p$ spaces with $ 1\le p<\infty $. Applications to the case of Hörmander-Mihlin multipliers, singular integral operators and Bochner-Riesz sums are given.