A new estimate for Bochner-Riesz operators at the critical index on the weighted Hardy spaces

Abstract

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.