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Fourier multipliers for Hardy spaces on graded Lie groups
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 5 / October 2023
- Published online by Cambridge University Press:
- 02 November 2022, pp. 1729-1750
- Print publication:
- October 2023
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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.
