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

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 - 2021

Keywords

Analysis on Lie groups
Fourier multipliers
Graded nilpotent Lie groups

ASJC Scopus subject areas

Mathematics(all)

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

Cite this

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abstract = "We study multipliers on graded nilpotent Lie groups defined via group Fourier transform. More precisely, we show that H{\"o}rmander-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.",

keywords = "Analysis on Lie groups, Fourier multipliers, Graded nilpotent Lie groups",

author = "V{\'e}ronique Fischer and Michael Ruzhansky",

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: {\textcopyright} Instytut Matematyczny PAN, 2021. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

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