An $H^1$ multiplier theorem on anisotropic spaces

A parallel result of (the classical) Sledd–Stegenga’s $H^1\to L^1$ multiplier theorem was obtained on the $H^1$ space under the anisotropic settings. Based on the same technique, an $H^1\to L^p$ multiplier theorem is also proved for $1\le p<\mathrm{\infty }$.