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arXiv · 1103.1821

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

Hua Wang
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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 $T^δ_R$ 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 $δ=n/p-(n+1)/2$. This result is new even in the unweighted case.

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Hua Wang. 2012-07-25. A new estimate for Bochner-Riesz operators at the critical index on the weighted Hardy spaces. https://arxiv.org/abs/1103.1821

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