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Fourier multipliers for Hardy spaces on graded Lie groups

Part of: Harmonic analysis in several variables Abstract harmonic analysis

Published online by Cambridge University Press:  02 November 2022

Qing Hong ,
Guorong Hu  and
Michael Ruzhansky
Qing Hong
Affiliation:
School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China (qhong@mail.bnu.edu.cn)
Guorong Hu
Affiliation:
School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China (qhong@mail.bnu.edu.cn)
Michael Ruzhansky
Affiliation:
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, B 9000 Ghent, Belgium School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom (Michael.Ruzhansky@UGent.be)
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Abstract

In this paper, we investigate the $H^{p}(G) \rightarrow L^{p}(G)$, $0< p \leq 1$, boundedness of multiplier operators defined via group Fourier transform on a graded Lie group $G$, where $H^{p}(G)$ is the Hardy space on $G$. Our main result extends those obtained in [Colloq. Math. 165 (2021), 1–30], where the $L^{1}(G)\rightarrow L^{1,\infty }(G)$ and $L^{p}(G) \rightarrow L^{p}(G)$, $1< p <\infty$, boundedness of such Fourier multiplier operators were proved.

Keywords

Graded nilpotent Lie groupsrepresentations of Lie groupsFourier multipliersHardy spaces

MSC classification

Primary: 43A80: Analysis on other specific Lie groups
Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 42B30: $H^p$-spaces
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 5 , October 2023 , pp. 1729 - 1750
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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