  We present a multiplier theorem on anisotropic Hardy spaces. When $m$
satisfies the anisotropic, pointwise Mihlin condition, we obtain boundedness of
the multiplier operator $T_m : H_A^p (\mathbb{R}^n) \rightarrow H_A^p
(\mathbb{R}^n)$, for the range of $p$ that depends on the eccentricities of the
dilation $A$ and the level of regularity of a multiplier symbol $m$. This
extends the classical multiplier theorem of Taibleson and Weiss.
