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arXiv · 1411.6950

Fourier multipliers on graded Lie groups

Veronique Fischer·Michael Ruzhansky
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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 $L^p$-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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Veronique Fischer, Michael Ruzhansky. 2014-11-25. Fourier multipliers on graded Lie groups. https://arxiv.org/abs/1411.6950

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