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 | |
| 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.
Funding
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.
Keywords
- Analysis on Lie groups
- Fourier multipliers
- Graded nilpotent Lie groups
ASJC Scopus subject areas
- General Mathematics