The boundedness of Bochner-Riesz operators on the weighted weak Hardy spaces

Abstract

Let $w$ be a Muckenhoupt weight and $W{H}_w^p({\mathbb{R}}^n)$ be the weighted weak Hardy spaces. In this paper, by using the atomic decomposition of $W{H}_w^p({\mathbb{R}}^n)$, we will show that the maximal Bochner-Riesz operators $T_{\ast }^{\delta }$ are bounded from $W{H}_w^p({\mathbb{R}}^n)$ to $W{L}_w^p({\mathbb{R}}^n)$ when $0<p\le 1$ and $\delta >n/p-(n+1)/2$. Moreover, we will also prove that the Bochner-Riesz operators $T_R^{\delta }$ are bounded on $W{H}_w^p({\mathbb{R}}^n)$ for $0<p\le 1$ and $\delta >n/p-(n+1)/2$. Our results are new even in the unweighted case.

arXiv comment15 pages. arXiv admin note: substantial text overlap with arXiv:1111.1387