Fourier multipliers on graded Lie groups

2014/11/25 by Veronique Fischer, Michael Ruzhansky, Fischer, Veronique +1
Mathematics · #22E30 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 43A22 #Representation Theory (math.RT) #Secondary: 43A15 #math.FA #math.RT #msc:22E30 #msc:43A15 #msc:43A22

paper · pdf · doi:10.48550/arxiv.1411.6950

23 pages

arxiv created 2020/06/15 · arxiv updated 2020/06/16

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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