  Let $w$ be a Muckenhoupt weight and $H^p_w(\mathbb R^n)$ be the weighted
Hardy spaces. In this paper, by using the atomic decomposition of
$H^p_w(\mathbb R^n)$, we will show that the Bochner-Riesz operators
$T^\delta_R$ are bounded from $H^p_w(\mathbb R^n)$ to the weighted weak Hardy
spaces $WH^p_w(\mathbb R^n)$ when $0<p<1$ and $\delta=n/p-(n+1)/2$. This result
is new even in the unweighted case.
