Fourier multipliers on graded lie groups

Véronique Fischer; Michael Ruzhansky

doi:10.4064/cm7817-6-2020

Fourier multipliers on graded lie groups

Véronique Fischer, Michael Ruzhansky

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Abstract

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 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.

Original language	English
Pages (from-to)	1-30
Number of pages	30
Journal	Colloquium Mathematicum
Volume	165
Issue number	1
Early online date	29 Oct 2020
DOIs	https://doi.org/10.4064/cm7817-6-2020
Publication status	Published - 31 Dec 2020

Bibliographical note

Funding Information:
Acknowledgements. The authors were supported by the EPSRC grant EP/K039407/1. The second author would also like to acknowledge the subsequent support by FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations, EPSRC grant EP/R003025/1, and LEVERHULME grant RPG-2017-151.

Publisher Copyright:
© Instytut Matematyczny PAN, 2021.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

Analysis on Lie groups
Fourier multipliers
Graded nilpotent Lie groups

ASJC Scopus subject areas

General Mathematics

Access to Document

10.4064/cm7817-6-2020

1411.6950.PDF
This is the author accepted manuscript of an article published in final form as Fischer, V & Ruzhansky, M 2021, 'Fourier multipliers on graded lie groups', Colloquium Mathematicum, vol. 165, no. 1, pp. 1-30. and available online via: https://doi.org/10.4064/cm7817-6-2020
Accepted author manuscript, 319 KB

https://arxiv.org/abs/1411.6950

Cite this

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N2 - 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 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.

AB - 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 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.

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Fourier multipliers on graded lie groups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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