Fourier multipliers on graded Lie groups

2014/11/25 by Fischer, Veronique, Ruzhansky, Michael
#22E30 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 43A22 #Representation Theory (math.RT) #Secondary: 43A15

paper · doi:10.48550/arxiv.1411.6950

Abstract

In this paper we study multipliers on graded nilpotent Lie groups defined via group Fourier transform. More precisely, we show that Hörmander 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.

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