A New Estimate for Bochner-Riesz Operators at the Critical Index on Weighted Hardy Spaces (Analysis in Theory and Applications, 2013)
Let $w$ be a Muckenhoupt weight and $H^p_w(\mathbb R^n)$ be the weighted Hardy space. In this paper, by using the atomic decomposition of $H^p_w(\mathbb R^n)$, we will show that the Bochner-Riesz operators $T^δ_R$ are bounded from $H^p_w(\mathbb R^n)$ to the weighted weak Hardy spaces $WH^p_w(\mathbb R^n)$ for $0 < p < 1$ and $δ=n/p-(n+1)/2$. This result is new even in the unweighted case.
Keywords: Bochner-Riesz operator; weighted Hardy space; weighted weak Hardy space; $A_p$ weight; atomic decomposition.