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. 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.