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

Abstract

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

arXiv comment13 pages. arXiv admin note: substantial text overlap with arXiv:1111.1388, arXiv:1111.5075, arXiv:1111.4269