%0 Journal Article
%T Fourier multipliers on graded Lie groups
%A Veronique Fischer
%A Michael Ruzhansky
%J Mathematics
%D 2014
%I arXiv
%X We study the $L^p$-boundedness of Fourier multipliers defined on graded nilpotent Lie groups via their group Fourier transform. We show that H\"ormander type conditions on the Fourier multipliers imply $L^p$-boundedness. We express these conditions using difference operators and positive Rockland operators. We also obtain a more refined condition using Sobolev spaces on the dual of the group which are defined and studied in this paper.
%U http://arxiv.org/abs/1411.6950v1