  Let $0 < p \leq 1$ and $w$ in the Muckenhoupt class $A_1$. Recently, by using
the weighted atomic decomposition and molecular characterization; Lee, Lin and
Yang \cite{LLY} (J. Math. Anal. Appl. 301 (2005), 394--400) established that
the Riesz transforms $R_j, j=1, 2,...,n$, are bounded on $H^p_w(\mathbb R^n)$.
In this note we extend this to the general case of weight $w$ in the
Muckenhoupt class $A_\infty$ through molecular characterization. One
difficulty, which has not been taken care in \cite{LLY}, consists in passing
from atoms to all functions in $H^p_w(\mathbb R^n)$. Furthermore, the
$H^p_w$-boundedness of $\theta$-Calder\'on-Zygmund operators are also given
through molecular characterization and atomic decomposition.
