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Fourier multipliers on graded Lie groups (1411.6950v2)
Published 25 Nov 2014 in math.FA and math.RT
Abstract: In this paper we study multipliers on graded nilpotent Lie groups defined via group Fourier transform. More precisely, we show that H\"ormander type conditions on the Fourier multipliers imply $Lp$-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.