Fourier multipliers for Hardy spaces on graded Lie groups

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. \textbf{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.